Práctica 1. Aprendizaje Automático¶

Authors: Carlos Iborra Llopis (100451170), Alejandra Galán Arrospide (100451273)

0. Table of contents¶

  • Práctica 1. Aprendizaje Automático
    • 0. Table of contents
    • 1. Requirements
    • 2. Reading the datasets
    • 3. Exploratory Data Analysis

1. Requirements¶

In [2]:
""" Importing necessary libraries """
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import missingno as msno
import seaborn as sns
import scipy.stats as st
import scipy
import sklearn

from matplotlib.cbook import boxplot_stats as bps

1.1. Cleaning ../data/img/ folder¶

This way we avoid creating multiple images and sending the old ones to the trash.
Also using this to upload cleaner commits to GitHub.

In [3]:
""" Cleaning the ../data/img/ folder """
import os
import glob

files = glob.glob('../data/img/*')
for f in files:
    if os.path.isfile(f) and f.endswith('.png'):
        os.remove(f)

files = glob.glob('../data/img/box-plot/*')
for f in files:
    if os.path.isfile(f) and f.endswith('.png'):
        os.remove(f)

2. Reading the datasets¶

Reading the datasets from the bz2 files, group 2.

In [4]:
""" Reading the dataset """
disp_df = pd.read_csv("../data/disp_st2ns1.txt.bz2",
                      compression="bz2", index_col=0)
comp_df = pd.read_csv("../data/comp_st2ns1.txt.bz2",
                      compression="bz2", index_col=0)

3. EDA¶

Key Concepts of Exploratory Data Analysis

  • 2 types of Data Analysis
    • Confirmatory Data Analysis
    • Exploratory Data Analysis
  • 4 Objectives of EDA
    • Discover Patterns
    • Spot Anomalies
    • Frame Hypothesis
    • Check Assumptions
  • 2 methods for exploration
    • Univariate Analysis
    • Bivariate Analysis
  • Stuff done during EDA
    • Trends
    • Distribution
    • Mean
    • Median
    • Outlier
    • Spread measurement (SD)
    • Correlations
    • Hypothesis testing
    • Visual Exploration
In [ ]:
 

3.0. Dataset preparation¶

In order to study with the EDA the real data we have, we will first prepare the data. We will do this by dividing prematurely the data into training and test sets. This will allow us to study the data in a more realistic way, since we will be able to study the data in the training set and then test the results in the test set. This way we will study and in a more realistic way the data we have.

In [5]:
""" Train Test Split (time series) """

# * Make a copy of the dataframe (as Padas dataframe is mutable, therefore uses a reference)
disp_df_copy = disp_df.copy()

# print(disp_df)
# print(disp_df_copy)

# Now we make the train_x, train_y, test_x, test_y splits taking into account the time series
# Note: the time series is ordered by date, therefore we need to split the data in a way that the train data is before the test data
# Note: the 10 first years are used for training and the last two years for testing
# Note: this is done because if not, we will be predicting the past from the future, which leads to errors and overfitting (data leakage) in the model

# * Calculate the number of rows for training and testing
num_rows = disp_df_copy.shape[0]
num_train_rows = int(num_rows * 10/12)  # 10 first years for training, 2 last years for testing

# * Split the data into train and test dataframes (using iloc instead of train_test_split as it picks random rows)
train_df = disp_df_copy.iloc[:num_train_rows, :]  # train contains the first 10 years of rows
test_df = disp_df_copy.iloc[num_train_rows:, :] # test contains the last 2 years of rows

# Print the number of rows for each dataframe
print(f"Number of rows for training: {train_df.shape[0]}")
print(f"Number of rows for testing: {test_df.shape[0]}")


# ! We maintain the original dataframe for later use (as we will divide it into train and test dataframes below)
# ! For the EDA, we will use the train_df dataframe (with the outpout variable).
Number of rows for training: 3650
Number of rows for testing: 730

3.1. Dataset description¶

  • apcp_sfc: 3-Hour accumulated precipitation at the surface (kg·m⁽⁻²⁾)
  • dlwrf_sfc: Downward long-wave radiative flux average at the surface (W·m⁽⁻²⁾)
  • dswrf_sfc: Downward short-wave radiative flux average at the surface (W·m⁽⁻²⁾)
  • pres_msl: Air pressure at mean sea level (Pa)
  • pwat_eatm: Precipitable Water over the entire depth of the atmosphere (kg·m⁽⁻²⁾)
  • spfh_2m: Specific Humidity at 2 m above ground (kg·kg⁽⁻¹⁾)
  • tcdc_eatm: Total cloud cover over the entire depth of the atmosphere (%)
  • tcolc_eatm: Total column-integrated condensate over the entire atmos. (kg·m⁽⁻²⁾)
  • tmax_2m: Maximum Temperature over the past 3 hours at 2 m above the ground (K)
  • tmin_2m: Mininmum Temperature over the past 3 hours at 2 m above the ground (K)
  • tmp_2m: Current temperature at 2 m above the ground (K)
  • tmp_sfc: Temperature of the surface (K)
  • ulwrf_sfc: Upward long-wave radiation at the surface (W·m⁽⁻²⁾)
  • ulwrf_tatm: Upward long-wave radiation at the top of the atmosphere (W·m⁽⁻²⁾)
  • uswrf_sfc: Upward short-wave radiation at the surface (W·m⁽⁻²⁾)
In [6]:
# Display all the columns of the dataframe
pd.set_option('display.max_columns', None)

train_df.describe()
Out[6]:
apcp_sf1_1 apcp_sf2_1 apcp_sf3_1 apcp_sf4_1 apcp_sf5_1 dlwrf_s1_1 dlwrf_s2_1 dlwrf_s3_1 dlwrf_s4_1 dlwrf_s5_1 dswrf_s1_1 dswrf_s2_1 dswrf_s3_1 dswrf_s4_1 dswrf_s5_1 pres_ms1_1 pres_ms2_1 pres_ms3_1 pres_ms4_1 pres_ms5_1 pwat_ea1_1 pwat_ea2_1 pwat_ea3_1 pwat_ea4_1 pwat_ea5_1 spfh_2m1_1 spfh_2m2_1 spfh_2m3_1 spfh_2m4_1 spfh_2m5_1 tcdc_ea1_1 tcdc_ea2_1 tcdc_ea3_1 tcdc_ea4_1 tcdc_ea5_1 tcolc_e1_1 tcolc_e2_1 tcolc_e3_1 tcolc_e4_1 tcolc_e5_1 tmax_2m1_1 tmax_2m2_1 tmax_2m3_1 tmax_2m4_1 tmax_2m5_1 tmin_2m1_1 tmin_2m2_1 tmin_2m3_1 tmin_2m4_1 tmin_2m5_1 tmp_2m_1_1 tmp_2m_2_1 tmp_2m_3_1 tmp_2m_4_1 tmp_2m_5_1 tmp_sfc1_1 tmp_sfc2_1 tmp_sfc3_1 tmp_sfc4_1 tmp_sfc5_1 ulwrf_s1_1 ulwrf_s2_1 ulwrf_s3_1 ulwrf_s4_1 ulwrf_s5_1 ulwrf_t1_1 ulwrf_t2_1 ulwrf_t3_1 ulwrf_t4_1 ulwrf_t5_1 uswrf_s1_1 uswrf_s2_1 uswrf_s3_1 uswrf_s4_1 uswrf_s5_1 salida
count 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3.650000e+03
mean 0.610222 0.251049 0.479367 0.279969 0.525625 316.590458 316.996492 324.225574 343.169304 342.582550 0.074371 163.928966 376.718929 686.534869 508.429988 101718.580471 101774.517076 101743.013770 101538.253073 101499.397514 21.394485 21.536129 22.127195 22.595594 22.384870 0.007844 0.008848 0.009356 0.009473 0.009918 0.069240 0.067845 0.064862 0.065706 0.062366 0.069539 0.068172 0.065166 0.066036 0.062748 286.950030 288.292227 292.803749 294.483694 294.542492 284.595935 284.638684 284.617400 292.733513 291.084714 284.846286 288.227387 292.740802 294.299550 291.301035 284.094056 289.230769 295.533258 295.904819 290.366407 375.991521 381.989673 400.742449 439.104661 431.318749 247.736467 247.626828 251.950057 262.207928 261.074238 0.078107 38.716712 76.394795 127.098207 99.476613 1.638200e+07
std 2.245850 0.994112 1.756408 1.120933 1.931408 56.119896 58.129352 58.941747 61.150202 61.027007 0.305126 112.645372 159.486316 227.642854 193.753483 725.206610 731.500969 720.701217 699.477989 715.361146 12.256253 12.358856 12.583364 12.633154 12.401121 0.004398 0.005039 0.005175 0.005097 0.005456 0.167104 0.169653 0.171287 0.172516 0.166113 0.166989 0.169522 0.171172 0.172385 0.165958 8.925065 9.743169 9.898253 9.789117 9.776615 8.735982 8.862301 8.866503 9.950300 10.099684 8.722593 9.795209 9.944761 9.795537 10.083859 8.861650 9.756852 9.148308 9.317363 10.462108 46.586515 49.914820 50.766618 53.159310 54.417631 36.270918 36.289003 35.798277 38.698726 38.427066 0.258752 26.010130 30.743175 40.765618 35.505727 8.059674e+06
min 0.000000 0.000000 0.000000 0.000000 0.000000 158.971770 160.032903 165.524543 183.671312 186.342961 0.000000 0.000000 20.000000 30.000000 20.000000 99316.970881 99315.887074 99327.755682 99040.100852 98830.153409 1.100000 1.314819 1.107352 1.142803 1.201246 0.000462 0.000485 0.000451 0.000478 0.000468 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 254.589220 254.937418 258.549777 260.800365 260.863475 251.941358 249.576132 249.576714 258.698331 258.171345 251.942065 254.844406 258.552646 260.795430 258.170049 250.100794 256.360800 263.634377 264.533564 256.520408 229.296161 223.985486 246.314349 278.576630 271.707606 104.671267 113.559602 118.679132 119.393449 121.951425 0.000000 0.000000 3.181818 4.363636 2.545455 5.100000e+05
25% 0.000000 0.000000 0.000000 0.000000 0.000000 270.043573 267.583016 275.008281 292.786299 291.777096 0.000000 52.727273 240.000000 525.454545 344.477273 101266.472124 101311.399680 101283.033381 101102.175426 101049.033203 10.879000 10.718024 11.122964 11.558385 11.559638 0.003991 0.004229 0.004617 0.004736 0.004754 0.000000 0.000000 0.000000 0.000000 0.000000 0.000618 0.000564 0.000545 0.000673 0.000727 280.127903 280.413352 284.916120 286.996939 287.043590 277.844468 277.666665 277.653641 284.828555 283.228638 278.075898 280.285865 284.764714 286.841753 283.495367 277.025516 281.298508 288.689326 288.982901 281.922856 338.180517 340.208757 358.706337 398.061333 388.214025 230.536257 230.759227 234.398558 246.594118 244.431134 0.000000 14.000000 53.818182 108.818182 74.909091 1.061385e+07
50% 0.000000 0.000000 0.000000 0.000000 0.000000 319.801794 321.400251 328.456741 345.402277 345.107513 0.000000 150.000000 384.318182 730.000000 525.636364 101645.975852 101704.351207 101674.750000 101472.419389 101425.127131 19.191209 19.163636 19.650000 20.290909 20.194252 0.007246 0.008248 0.008909 0.009156 0.009518 0.004545 0.004545 0.003636 0.003636 0.002727 0.005118 0.004855 0.004145 0.004345 0.003673 287.597683 289.039583 293.757317 295.529044 295.598358 285.070623 285.192374 285.106049 293.606805 291.806785 285.381022 288.990954 293.704959 295.310534 292.050580 284.581711 290.050444 296.204518 296.669453 291.126846 376.267101 382.791372 401.524648 440.987373 433.520339 253.350231 253.394166 257.342928 270.790095 269.287814 0.000000 35.500000 79.636364 136.636364 105.454545 1.638195e+07
75% 0.114545 0.051818 0.121591 0.033636 0.090000 367.134144 370.342597 378.683015 399.545104 398.891589 0.000000 264.454545 524.636364 893.636364 693.681818 102131.380504 102188.719283 102148.666726 101940.005327 101919.873402 31.188882 31.471632 32.439831 33.103788 32.459132 0.011612 0.013523 0.014275 0.014169 0.015062 0.055455 0.056364 0.042727 0.043636 0.038182 0.056136 0.056918 0.042900 0.043523 0.038843 294.329548 296.940075 301.377123 302.732298 302.753016 292.290495 292.587547 292.576612 301.351051 299.909759 292.551771 296.945783 301.346064 302.621007 300.068969 292.110791 297.882618 303.161016 303.555412 299.639197 416.508387 427.792698 445.458675 482.899051 476.327880 274.309069 274.750930 278.752231 289.945510 289.588822 0.000000 62.000000 103.068182 155.454545 129.727273 2.329185e+07
max 34.428182 16.846364 28.399091 26.381818 36.875455 426.173970 427.486894 429.693146 455.566337 453.910406 3.000000 381.818182 642.181818 990.000000 791.090909 104688.396307 104856.285511 104693.185369 104244.932528 104249.968040 60.327273 58.876881 59.915362 59.309182 60.529133 0.018809 0.019533 0.020985 0.021932 0.023318 1.920909 2.370000 2.449091 2.146364 1.957273 1.920136 2.369282 2.450482 2.146409 1.956655 304.480122 304.792880 311.277519 312.660564 312.668726 300.350930 299.724509 299.735546 310.815957 308.761763 300.344230 304.773410 311.272270 312.595520 308.827304 299.869093 306.834309 315.964081 313.965757 308.270147 470.753102 469.429213 504.584351 555.704024 542.529280 318.245345 311.991660 315.569164 328.920274 327.253141 1.000000 92.272727 192.636364 450.636364 313.909091 3.122700e+07
In [7]:
train_df.shape
Out[7]:
(3650, 76)
In [8]:
train_df.head()
Out[8]:
apcp_sf1_1 apcp_sf2_1 apcp_sf3_1 apcp_sf4_1 apcp_sf5_1 dlwrf_s1_1 dlwrf_s2_1 dlwrf_s3_1 dlwrf_s4_1 dlwrf_s5_1 dswrf_s1_1 dswrf_s2_1 dswrf_s3_1 dswrf_s4_1 dswrf_s5_1 pres_ms1_1 pres_ms2_1 pres_ms3_1 pres_ms4_1 pres_ms5_1 pwat_ea1_1 pwat_ea2_1 pwat_ea3_1 pwat_ea4_1 pwat_ea5_1 spfh_2m1_1 spfh_2m2_1 spfh_2m3_1 spfh_2m4_1 spfh_2m5_1 tcdc_ea1_1 tcdc_ea2_1 tcdc_ea3_1 tcdc_ea4_1 tcdc_ea5_1 tcolc_e1_1 tcolc_e2_1 tcolc_e3_1 tcolc_e4_1 tcolc_e5_1 tmax_2m1_1 tmax_2m2_1 tmax_2m3_1 tmax_2m4_1 tmax_2m5_1 tmin_2m1_1 tmin_2m2_1 tmin_2m3_1 tmin_2m4_1 tmin_2m5_1 tmp_2m_1_1 tmp_2m_2_1 tmp_2m_3_1 tmp_2m_4_1 tmp_2m_5_1 tmp_sfc1_1 tmp_sfc2_1 tmp_sfc3_1 tmp_sfc4_1 tmp_sfc5_1 ulwrf_s1_1 ulwrf_s2_1 ulwrf_s3_1 ulwrf_s4_1 ulwrf_s5_1 ulwrf_t1_1 ulwrf_t2_1 ulwrf_t3_1 ulwrf_t4_1 ulwrf_t5_1 uswrf_s1_1 uswrf_s2_1 uswrf_s3_1 uswrf_s4_1 uswrf_s5_1 salida
V1 0.0 0.0 0.0 0.000000 0.0 268.583582 244.241641 251.174486 269.741308 268.377441 0.0 30.0 220.000000 510.000000 330.000000 101832.056108 102053.159091 102090.046165 101934.175426 101988.003551 5.879193 7.018182 8.460800 9.418182 9.727869 0.003229 0.002993 0.003775 0.003870 0.003855 0.000000 0.000000 0.000000 0.000000 0.000909 0.000818 0.000264 0.000255 0.000500 0.002218 280.789784 279.627444 285.727761 286.881681 286.885823 279.198020 278.472615 278.474720 285.799685 280.966961 279.249256 279.612202 285.742784 286.841053 280.960865 277.278370 279.250383 288.826760 288.596086 278.500078 341.122231 335.067918 354.626126 397.774053 383.281225 222.153166 252.504475 254.760271 263.342404 260.067843 0.0 10.000000 50.000000 106.636364 72.000000 11930700
V2 0.0 0.0 0.0 0.008182 0.2 251.725869 255.824126 272.163913 318.259924 307.929083 0.0 30.0 173.636364 333.636364 224.545455 101425.883523 101284.509233 101253.654830 100999.313920 101424.626420 12.534339 11.987316 12.159355 12.313590 13.469729 0.003737 0.003931 0.004015 0.003994 0.004826 0.037273 0.021818 0.101818 0.084545 0.109091 0.037155 0.021309 0.102373 0.085827 0.109336 278.822329 278.063379 283.618583 286.606684 286.643397 277.258919 276.740628 276.740628 283.687009 282.111078 277.282621 278.070390 283.604600 286.554729 282.105011 275.830009 278.269459 287.048970 287.325478 281.005252 330.159915 329.354673 347.524819 388.017767 378.773804 236.836691 233.458263 233.027276 212.652054 222.052916 0.0 8.181818 35.909091 58.181818 42.090909 9778500
V3 0.0 0.0 0.0 0.000000 0.0 219.734547 211.996022 216.405820 235.529123 239.840132 0.0 30.0 220.000000 523.636364 337.545455 102253.654119 102301.918324 102088.093750 101652.815341 101543.146307 5.726770 5.458528 5.700000 7.163636 9.536364 0.002003 0.001919 0.002107 0.002431 0.002583 0.000000 0.000000 0.007273 0.007273 0.042727 0.001427 0.001582 0.007309 0.006973 0.042127 275.400091 270.222512 275.885787 279.049513 279.381653 269.756037 269.157731 269.156439 276.041792 275.301960 269.766876 270.204285 275.880818 279.064603 275.806757 269.533059 271.690993 281.759993 282.686446 273.615503 309.639845 299.751961 317.250763 364.339136 351.496665 238.655654 232.828737 235.480750 245.177331 238.893102 0.0 10.272727 55.272727 118.454545 79.181818 9771900
V4 0.0 0.0 0.0 0.000000 0.0 253.499410 230.896544 235.857221 240.274556 237.804048 0.0 30.0 208.181818 512.727273 337.181818 102110.375710 102435.603693 102688.528409 102588.876420 102598.252841 7.889904 6.768959 6.208357 5.977267 6.411838 0.002918 0.002735 0.002771 0.002821 0.002738 0.000000 0.002727 0.005455 0.000909 0.012727 0.000473 0.004018 0.007300 0.001600 0.014882 279.396046 276.176919 276.868630 278.550368 278.572038 276.175482 273.839142 273.840535 276.942990 273.802970 276.312428 274.045715 276.877749 278.571555 273.812827 274.824765 274.466433 281.291418 281.871679 272.191753 330.310971 318.761563 329.305478 360.297788 348.618319 236.784869 241.916776 243.398572 251.473036 247.503769 0.0 8.909091 46.000000 107.090909 73.636364 6466800
V5 0.0 0.0 0.0 0.000000 0.0 234.890020 238.927051 246.850822 271.577246 275.572826 0.0 30.0 220.000000 517.272727 336.363636 101750.317472 101331.333807 100921.029119 100422.514915 100309.059659 10.783448 10.425542 10.362327 8.829511 9.647615 0.003274 0.003269 0.003066 0.003483 0.003788 0.000909 0.000909 0.000909 0.014545 0.050909 0.001673 0.001836 0.001373 0.015909 0.049591 273.294803 275.018022 283.542744 288.171156 288.265137 272.858415 273.303902 273.306355 283.734819 283.735446 273.314844 274.990234 283.563099 288.178922 285.567946 272.260426 275.132668 285.698725 288.490562 283.121391 310.023179 314.763264 334.042186 388.737835 383.409776 233.641681 233.706659 239.952805 258.128188 253.200684 0.0 8.909091 48.909091 106.272727 71.818182 11545200
In [9]:
train_df.info()
<class 'pandas.core.frame.DataFrame'>
Index: 3650 entries, V1 to V3650
Data columns (total 76 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   apcp_sf1_1  3650 non-null   float64
 1   apcp_sf2_1  3650 non-null   float64
 2   apcp_sf3_1  3650 non-null   float64
 3   apcp_sf4_1  3650 non-null   float64
 4   apcp_sf5_1  3650 non-null   float64
 5   dlwrf_s1_1  3650 non-null   float64
 6   dlwrf_s2_1  3650 non-null   float64
 7   dlwrf_s3_1  3650 non-null   float64
 8   dlwrf_s4_1  3650 non-null   float64
 9   dlwrf_s5_1  3650 non-null   float64
 10  dswrf_s1_1  3650 non-null   float64
 11  dswrf_s2_1  3650 non-null   float64
 12  dswrf_s3_1  3650 non-null   float64
 13  dswrf_s4_1  3650 non-null   float64
 14  dswrf_s5_1  3650 non-null   float64
 15  pres_ms1_1  3650 non-null   float64
 16  pres_ms2_1  3650 non-null   float64
 17  pres_ms3_1  3650 non-null   float64
 18  pres_ms4_1  3650 non-null   float64
 19  pres_ms5_1  3650 non-null   float64
 20  pwat_ea1_1  3650 non-null   float64
 21  pwat_ea2_1  3650 non-null   float64
 22  pwat_ea3_1  3650 non-null   float64
 23  pwat_ea4_1  3650 non-null   float64
 24  pwat_ea5_1  3650 non-null   float64
 25  spfh_2m1_1  3650 non-null   float64
 26  spfh_2m2_1  3650 non-null   float64
 27  spfh_2m3_1  3650 non-null   float64
 28  spfh_2m4_1  3650 non-null   float64
 29  spfh_2m5_1  3650 non-null   float64
 30  tcdc_ea1_1  3650 non-null   float64
 31  tcdc_ea2_1  3650 non-null   float64
 32  tcdc_ea3_1  3650 non-null   float64
 33  tcdc_ea4_1  3650 non-null   float64
 34  tcdc_ea5_1  3650 non-null   float64
 35  tcolc_e1_1  3650 non-null   float64
 36  tcolc_e2_1  3650 non-null   float64
 37  tcolc_e3_1  3650 non-null   float64
 38  tcolc_e4_1  3650 non-null   float64
 39  tcolc_e5_1  3650 non-null   float64
 40  tmax_2m1_1  3650 non-null   float64
 41  tmax_2m2_1  3650 non-null   float64
 42  tmax_2m3_1  3650 non-null   float64
 43  tmax_2m4_1  3650 non-null   float64
 44  tmax_2m5_1  3650 non-null   float64
 45  tmin_2m1_1  3650 non-null   float64
 46  tmin_2m2_1  3650 non-null   float64
 47  tmin_2m3_1  3650 non-null   float64
 48  tmin_2m4_1  3650 non-null   float64
 49  tmin_2m5_1  3650 non-null   float64
 50  tmp_2m_1_1  3650 non-null   float64
 51  tmp_2m_2_1  3650 non-null   float64
 52  tmp_2m_3_1  3650 non-null   float64
 53  tmp_2m_4_1  3650 non-null   float64
 54  tmp_2m_5_1  3650 non-null   float64
 55  tmp_sfc1_1  3650 non-null   float64
 56  tmp_sfc2_1  3650 non-null   float64
 57  tmp_sfc3_1  3650 non-null   float64
 58  tmp_sfc4_1  3650 non-null   float64
 59  tmp_sfc5_1  3650 non-null   float64
 60  ulwrf_s1_1  3650 non-null   float64
 61  ulwrf_s2_1  3650 non-null   float64
 62  ulwrf_s3_1  3650 non-null   float64
 63  ulwrf_s4_1  3650 non-null   float64
 64  ulwrf_s5_1  3650 non-null   float64
 65  ulwrf_t1_1  3650 non-null   float64
 66  ulwrf_t2_1  3650 non-null   float64
 67  ulwrf_t3_1  3650 non-null   float64
 68  ulwrf_t4_1  3650 non-null   float64
 69  ulwrf_t5_1  3650 non-null   float64
 70  uswrf_s1_1  3650 non-null   float64
 71  uswrf_s2_1  3650 non-null   float64
 72  uswrf_s3_1  3650 non-null   float64
 73  uswrf_s4_1  3650 non-null   float64
 74  uswrf_s5_1  3650 non-null   float64
 75  salida      3650 non-null   int64  
dtypes: float64(75), int64(1)
memory usage: 2.1+ MB

3.2. Missing values¶

Fist, we check the number the total number of missing values in the dataset in order to know if we have to clean the dataset or not.

In [10]:
train_df.isna().sum()
Out[10]:
apcp_sf1_1    0
apcp_sf2_1    0
apcp_sf3_1    0
apcp_sf4_1    0
apcp_sf5_1    0
             ..
uswrf_s2_1    0
uswrf_s3_1    0
uswrf_s4_1    0
uswrf_s5_1    0
salida        0
Length: 76, dtype: int64

As we can oberve, there are no missing values in the dataset, but theres still the possibility of having missing values measured as 0's, so we will check if all those zeros make sense in the context of the dataset or not.

In [11]:
# In the plot, we can see that there are a lot of 0 values in the dataset
train_df.plot(legend=False, figsize=(15, 5))
Out[11]:
<Axes: >
In [12]:
result = train_df.eq(0.0).sum()/len(train_df)*100

# Select those columns with more than 30% of zeros
result = result[result > 30.0]
result = result.sort_values(ascending=False)
result
Out[12]:
dswrf_s1_1    91.808219
uswrf_s1_1    90.767123
apcp_sf4_1    63.041096
apcp_sf5_1    61.041096
apcp_sf1_1    60.821918
apcp_sf2_1    59.890411
apcp_sf3_1    56.739726
tcdc_ea3_1    37.917808
tcdc_ea1_1    37.808219
tcdc_ea2_1    37.424658
tcdc_ea5_1    36.301370
tcdc_ea4_1    35.726027
dtype: float64

Observations¶

As output of the previous cell, we can see that there exist a lot of zeros in the dataset, let's analize if those zeros make sense or not.

The variables with most ammount of zeros (>30%) are:

  • dswrf_s1_1: Downward short-wave radiative flux average at the surface, at 12:00 UTC, normal to have a lot of zeros as it is not sunny at 12:00
  • uswrf_s1_1: Upward short-wave radiation at the surface, at 12:00 UTC, normal to have a lot of zeros as it is not sunny at 12:00
  • apcp_s: 3-Hour accumulated precipitation at the surface, as it is not raining every day, it is normal to have a lot of zeros
  • tcdc_ea: Total cloud cover over the entire depth of the atmosphere, as it is not cloudy every day, it is normal to have a lot of zeros

First, lets start by assigning the zeros to NaNs. By doing this we can visualize the varibles that take more values other than zero.

In [13]:
disp_df_nan = train_df.replace(0.0, np.nan)
In [14]:
""" Plotting missing values """
# Sustitute 0.0 values with NaN and plot the name of the columns with missing values
# ? msno.bar is a simple visualization of nullity by column
msno.bar(disp_df_nan, labels=True, fontsize=7, figsize=(15, 7))

# Exporting image as png to ../data/img folder
plt.savefig("../data/img/missing_values_bar.png")
In [15]:
""" Plotting the missing values in a matrix """

# Fix ValueError: keyword grid_b is not recognized



# ? The msno.matrix nullity matrix is a data-dense display which lets you quickly visually pick out patterns in data completion.
msno.matrix(disp_df_nan)

# Exporting image as png to ../data/img folder
plt.savefig("../data/img/missing_values_matrix.png")
In [16]:
""" Plotting the missing values in a heatmap """
# As in a hetmap not every value is shown, we must delimit the values to the ones with more than 30% of missing values
result = disp_df.eq(0.0).sum()/len(disp_df)*100
result = result[result > 30.0] # Select those columns with more than 30% of zeros
result = result.sort_values(ascending=False)
result = result.index.tolist() # Convert to list
result

# ? The missingno correlation heatmap measures nullity correlation: how strongly the presence or absence of one variable affects the presence of another
msno.heatmap(disp_df_nan[result], fontsize=7, figsize=(15, 7))

# Exporting image as png to ../data/img folder
plt.savefig("../data/img/missing_values_heatmap.png")
In [17]:
""" Plotting the dendrogram """

# ? The dendrogram allows you to more fully correlate variable completion, revealing trends deeper than the pairwise ones visible in the correlation heatmap:
msno.dendrogram(disp_df_nan, orientation="top",fontsize=7, figsize=(15, 7))

# Exporting image as png to ../data/img folder
plt.savefig("../data/img/missing_values_dendrogram.png")

Conclusions¶

In this section, we have observe that there are no attibutes with 'Null' nor 'NaN' nor 'None' values. This indicated that at a first glance, the data is clean, at least of those datatypes.

In second place, we have observed that the attributes that we suspected could have an important number of missing values (represented by 0 instead of the previously mentioned), had instead valuable information, as we have proved along this section.
Since the data is clean and we have concluded there are no missing values, we do not need to complete them using a model or other methods, so we can move on to the next step, observing the outliers.

3.3. Outliers¶

With the objective of noticing the outliers on each attribute, we create a box-plot of each of the attributes

In [18]:
list_of_attributes = train_df.columns.values.tolist()
#print(list_of_attributes)
In [19]:
# Boxplot with all attributes in the dataset
# sns.boxplot(data=train_df, orient="h")
# plt.show()
In [20]:
train_df.describe()
Out[20]:
apcp_sf1_1 apcp_sf2_1 apcp_sf3_1 apcp_sf4_1 apcp_sf5_1 dlwrf_s1_1 dlwrf_s2_1 dlwrf_s3_1 dlwrf_s4_1 dlwrf_s5_1 dswrf_s1_1 dswrf_s2_1 dswrf_s3_1 dswrf_s4_1 dswrf_s5_1 pres_ms1_1 pres_ms2_1 pres_ms3_1 pres_ms4_1 pres_ms5_1 pwat_ea1_1 pwat_ea2_1 pwat_ea3_1 pwat_ea4_1 pwat_ea5_1 spfh_2m1_1 spfh_2m2_1 spfh_2m3_1 spfh_2m4_1 spfh_2m5_1 tcdc_ea1_1 tcdc_ea2_1 tcdc_ea3_1 tcdc_ea4_1 tcdc_ea5_1 tcolc_e1_1 tcolc_e2_1 tcolc_e3_1 tcolc_e4_1 tcolc_e5_1 tmax_2m1_1 tmax_2m2_1 tmax_2m3_1 tmax_2m4_1 tmax_2m5_1 tmin_2m1_1 tmin_2m2_1 tmin_2m3_1 tmin_2m4_1 tmin_2m5_1 tmp_2m_1_1 tmp_2m_2_1 tmp_2m_3_1 tmp_2m_4_1 tmp_2m_5_1 tmp_sfc1_1 tmp_sfc2_1 tmp_sfc3_1 tmp_sfc4_1 tmp_sfc5_1 ulwrf_s1_1 ulwrf_s2_1 ulwrf_s3_1 ulwrf_s4_1 ulwrf_s5_1 ulwrf_t1_1 ulwrf_t2_1 ulwrf_t3_1 ulwrf_t4_1 ulwrf_t5_1 uswrf_s1_1 uswrf_s2_1 uswrf_s3_1 uswrf_s4_1 uswrf_s5_1 salida
count 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3650.000000 3.650000e+03
mean 0.610222 0.251049 0.479367 0.279969 0.525625 316.590458 316.996492 324.225574 343.169304 342.582550 0.074371 163.928966 376.718929 686.534869 508.429988 101718.580471 101774.517076 101743.013770 101538.253073 101499.397514 21.394485 21.536129 22.127195 22.595594 22.384870 0.007844 0.008848 0.009356 0.009473 0.009918 0.069240 0.067845 0.064862 0.065706 0.062366 0.069539 0.068172 0.065166 0.066036 0.062748 286.950030 288.292227 292.803749 294.483694 294.542492 284.595935 284.638684 284.617400 292.733513 291.084714 284.846286 288.227387 292.740802 294.299550 291.301035 284.094056 289.230769 295.533258 295.904819 290.366407 375.991521 381.989673 400.742449 439.104661 431.318749 247.736467 247.626828 251.950057 262.207928 261.074238 0.078107 38.716712 76.394795 127.098207 99.476613 1.638200e+07
std 2.245850 0.994112 1.756408 1.120933 1.931408 56.119896 58.129352 58.941747 61.150202 61.027007 0.305126 112.645372 159.486316 227.642854 193.753483 725.206610 731.500969 720.701217 699.477989 715.361146 12.256253 12.358856 12.583364 12.633154 12.401121 0.004398 0.005039 0.005175 0.005097 0.005456 0.167104 0.169653 0.171287 0.172516 0.166113 0.166989 0.169522 0.171172 0.172385 0.165958 8.925065 9.743169 9.898253 9.789117 9.776615 8.735982 8.862301 8.866503 9.950300 10.099684 8.722593 9.795209 9.944761 9.795537 10.083859 8.861650 9.756852 9.148308 9.317363 10.462108 46.586515 49.914820 50.766618 53.159310 54.417631 36.270918 36.289003 35.798277 38.698726 38.427066 0.258752 26.010130 30.743175 40.765618 35.505727 8.059674e+06
min 0.000000 0.000000 0.000000 0.000000 0.000000 158.971770 160.032903 165.524543 183.671312 186.342961 0.000000 0.000000 20.000000 30.000000 20.000000 99316.970881 99315.887074 99327.755682 99040.100852 98830.153409 1.100000 1.314819 1.107352 1.142803 1.201246 0.000462 0.000485 0.000451 0.000478 0.000468 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 254.589220 254.937418 258.549777 260.800365 260.863475 251.941358 249.576132 249.576714 258.698331 258.171345 251.942065 254.844406 258.552646 260.795430 258.170049 250.100794 256.360800 263.634377 264.533564 256.520408 229.296161 223.985486 246.314349 278.576630 271.707606 104.671267 113.559602 118.679132 119.393449 121.951425 0.000000 0.000000 3.181818 4.363636 2.545455 5.100000e+05
25% 0.000000 0.000000 0.000000 0.000000 0.000000 270.043573 267.583016 275.008281 292.786299 291.777096 0.000000 52.727273 240.000000 525.454545 344.477273 101266.472124 101311.399680 101283.033381 101102.175426 101049.033203 10.879000 10.718024 11.122964 11.558385 11.559638 0.003991 0.004229 0.004617 0.004736 0.004754 0.000000 0.000000 0.000000 0.000000 0.000000 0.000618 0.000564 0.000545 0.000673 0.000727 280.127903 280.413352 284.916120 286.996939 287.043590 277.844468 277.666665 277.653641 284.828555 283.228638 278.075898 280.285865 284.764714 286.841753 283.495367 277.025516 281.298508 288.689326 288.982901 281.922856 338.180517 340.208757 358.706337 398.061333 388.214025 230.536257 230.759227 234.398558 246.594118 244.431134 0.000000 14.000000 53.818182 108.818182 74.909091 1.061385e+07
50% 0.000000 0.000000 0.000000 0.000000 0.000000 319.801794 321.400251 328.456741 345.402277 345.107513 0.000000 150.000000 384.318182 730.000000 525.636364 101645.975852 101704.351207 101674.750000 101472.419389 101425.127131 19.191209 19.163636 19.650000 20.290909 20.194252 0.007246 0.008248 0.008909 0.009156 0.009518 0.004545 0.004545 0.003636 0.003636 0.002727 0.005118 0.004855 0.004145 0.004345 0.003673 287.597683 289.039583 293.757317 295.529044 295.598358 285.070623 285.192374 285.106049 293.606805 291.806785 285.381022 288.990954 293.704959 295.310534 292.050580 284.581711 290.050444 296.204518 296.669453 291.126846 376.267101 382.791372 401.524648 440.987373 433.520339 253.350231 253.394166 257.342928 270.790095 269.287814 0.000000 35.500000 79.636364 136.636364 105.454545 1.638195e+07
75% 0.114545 0.051818 0.121591 0.033636 0.090000 367.134144 370.342597 378.683015 399.545104 398.891589 0.000000 264.454545 524.636364 893.636364 693.681818 102131.380504 102188.719283 102148.666726 101940.005327 101919.873402 31.188882 31.471632 32.439831 33.103788 32.459132 0.011612 0.013523 0.014275 0.014169 0.015062 0.055455 0.056364 0.042727 0.043636 0.038182 0.056136 0.056918 0.042900 0.043523 0.038843 294.329548 296.940075 301.377123 302.732298 302.753016 292.290495 292.587547 292.576612 301.351051 299.909759 292.551771 296.945783 301.346064 302.621007 300.068969 292.110791 297.882618 303.161016 303.555412 299.639197 416.508387 427.792698 445.458675 482.899051 476.327880 274.309069 274.750930 278.752231 289.945510 289.588822 0.000000 62.000000 103.068182 155.454545 129.727273 2.329185e+07
max 34.428182 16.846364 28.399091 26.381818 36.875455 426.173970 427.486894 429.693146 455.566337 453.910406 3.000000 381.818182 642.181818 990.000000 791.090909 104688.396307 104856.285511 104693.185369 104244.932528 104249.968040 60.327273 58.876881 59.915362 59.309182 60.529133 0.018809 0.019533 0.020985 0.021932 0.023318 1.920909 2.370000 2.449091 2.146364 1.957273 1.920136 2.369282 2.450482 2.146409 1.956655 304.480122 304.792880 311.277519 312.660564 312.668726 300.350930 299.724509 299.735546 310.815957 308.761763 300.344230 304.773410 311.272270 312.595520 308.827304 299.869093 306.834309 315.964081 313.965757 308.270147 470.753102 469.429213 504.584351 555.704024 542.529280 318.245345 311.991660 315.569164 328.920274 327.253141 1.000000 92.272727 192.636364 450.636364 313.909091 3.122700e+07
In [21]:
train_df['apcp_sf1_1'].value_counts()
Out[21]:
0.000000    2220
0.000909      54
0.001818      24
0.003636      19
0.002727      19
            ... 
2.356364       1
0.920000       1
0.048182       1
0.211818       1
1.363636       1
Name: apcp_sf1_1, Length: 1170, dtype: int64

Here, by plotting the boxplots and making the outliers (fliers) visible, we are able to see some outliers in the dataset.
Take into account that the outliers are represented by the points outside the boxplot and they can be potentially wrong values or just values that are not usual in the dataset (ruido).

In [22]:
""" Plotting the boxplot for each attribute and getting the outliers of each attribute """
total_outliers = []
# * We iterate over the list of attributes
for attribute in list_of_attributes:
    # * sns.regplot(x=train_df[attribute], y=train_df['total'], fit_reg=False)
    sns.boxplot(data=train_df[attribute], x=train_df[attribute], orient="h")
    # * Use the command below to show each plot (small size for visualization sake)
    # sns.set(rc={'figure.figsize':(1,.5)})
    # plt.show()
    # * All the images are saved in the folder ../data/img/box-plot
    plt.savefig(f"../data/img/box-plot/{str(attribute)}.png")

    # We obtain the a list of outliers for each attribute
    list_of_outliers = train_df[attribute][train_df[attribute] > train_df[attribute].quantile(0.75) + 1.5*(train_df[attribute].quantile(0.75) - train_df[attribute].quantile(0.25))].tolist()
    outliers = [f'{attribute} outliers'] + [len(list_of_outliers)] + [list_of_outliers]
    # * In orde to print the total number of outliers for each attribute
    # print(f'{attribute} has {len(list_of_outliers)} outliers')
    # ! Data structure: [attribute, number of outliers, list of outliers]
    # print(outliers)
    total_outliers.append(outliers)

print(total_outliers)
print(len(total_outliers))
[['apcp_sf1_1 outliers', 693, [1.11909090930765, 0.358181819997051, 2.46363633329218, 0.510000003332442, 1.12363637577404, 26.886363549666, 0.942727267742157, 1.08727271990343, 11.872727134011, 0.358181823383678, 4.84181818095121, 6.9500000260093, 5.18909092382951, 7.09727272120389, 0.916363634846427, 0.448181818832051, 3.9127273153175, 3.16363642432473, 1.2427272695032, 2.06454543633894, 6.27000004188581, 1.0327272862196, 0.31909091161056, 2.17272726785053, 0.876363634724509, 2.17636364630678, 0.487272722815925, 1.37545453960245, 1.01727271080017, 0.504545454274524, 1.41818179122426, 8.4618182182312, 1.12727272510529, 4.05181815881621, 0.94454545324499, 4.33272725885565, 0.670000000433488, 0.358181819997051, 0.418181818994609, 10.9018183621493, 0.512727274474773, 3.700909094377, 5.45909088308161, 0.351818186992949, 1.35636362907561, 0.296363632787358, 0.409090909768235, 6.56000002947721, 6.44272729483518, 2.39000003039837, 1.08272727240216, 3.78181821649725, 0.45545454594222, 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76

We managed to create a list containing the name of the atribute, the number of outliers and the value of the outliers for each attribute, calculated by applying the IQR method.
This is relevant as we managed to create a 'total_outliers' variable that contains the list data structures of all the different outliers from all the attributes, so that it can be easily accessed in a future to remove the outliers from the dataset if needed for testing purposes.

As suspected, we can see that there are a lot of outliers in the dataset, therefore it is plausible that some of them are noise, thus possibly being removed in a future model in order to improve it.
Now, we need to analyze if they are the result of bad measurements or if they are significant data for the analysis.

In [23]:
""" Skewness """
# ? skewness: measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.
train_df.skew().sort_values(ascending=False)
Out[23]:
apcp_sf4_1    9.297678
apcp_sf2_1    7.610005
apcp_sf5_1    7.244491
apcp_sf3_1    7.241727
apcp_sf1_1    6.783553
                ...   
ulwrf_t1_1   -0.964701
ulwrf_t3_1   -0.989917
ulwrf_t2_1   -1.001763
ulwrf_t5_1   -1.071147
ulwrf_t4_1   -1.196425
Length: 76, dtype: float64
In [24]:
""" Kurtosis """
# ? kurtosis: measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
train_df.kurt().sort_values(ascending=False)
Out[24]:
apcp_sf4_1    138.601323
apcp_sf2_1     79.535762
apcp_sf5_1     78.321580
apcp_sf3_1     72.498316
apcp_sf1_1     61.204708
                 ...    
uswrf_s2_1     -1.306893
spfh_2m2_1     -1.320499
spfh_2m5_1     -1.321073
dswrf_s2_1     -1.323864
spfh_2m3_1     -1.329847
Length: 76, dtype: float64
In [25]:
y = train_df['apcp_sf4_1']
plt.figure(1); plt.title('Normal')
sns.distplot(y, kde=True, fit=st.norm)
plt.figure(2); plt.title('Log Normal')
sns.distplot(y, kde=True, fit=st.lognorm)
/tmp/ipykernel_5115/2851594757.py:3: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(y, kde=True, fit=st.norm)
/tmp/ipykernel_5115/2851594757.py:5: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(y, kde=True, fit=st.lognorm)
Out[25]:
<Axes: title={'center': 'Log Normal'}, xlabel='apcp_sf4_1', ylabel='Density'>
In [26]:
sns.distplot(train_df.skew(),color='blue',axlabel ='Skewness')
/tmp/ipykernel_5115/3675943835.py:1: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(train_df.skew(),color='blue',axlabel ='Skewness')
Out[26]:
<Axes: xlabel='Skewness', ylabel='Density'>
In [27]:
plt.figure(figsize = (12,8))
sns.distplot(train_df.kurt(),color='r',axlabel ='Kurtosis',norm_hist= False, kde = True,rug = False)
#plt.hist(train.kurt(),orientation = 'vertical',histtype = 'bar',label ='Kurtosis', color ='blue')
plt.show()
/tmp/ipykernel_5115/1886886254.py:2: UserWarning: 

`distplot` is a deprecated function and will be removed in seaborn v0.14.0.

Please adapt your code to use either `displot` (a figure-level function with
similar flexibility) or `histplot` (an axes-level function for histograms).

For a guide to updating your code to use the new functions, please see
https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751

  sns.distplot(train_df.kurt(),color='r',axlabel ='Kurtosis',norm_hist= False, kde = True,rug = False)

3.4. Correlation¶

In this section we are getting information about the correlation of the variables between them. This information is valuable in order to make good decisions when deleting redundant attributes. Also note we are getting information about the correlation between each attribute and the solution variable. This allows us to know the most relevant attributes, making the best decisions when creating the different models.

In [28]:
correlation = train_df.corr()
correlation = abs(correlation)
print(correlation.shape)  # 76 x 76 matrix of correlation values
(76, 76)

Getting the correlation matrix formatted into our own data structure¶

This is done for the sake of simplicity and to be able to visualize the correlation matrix in a more intuitive way.

In [29]:
correlation_list = []

for column in train_df:
    correlation[column] = abs(correlation[column])
    mask = correlation[column] > 0.95
    # print(correlation[column][mask].sort_values(ascending = False))
    
    # Translate the comment below to English: 
    # we add the correlation values to a list of lists, which contains the names of the correlated columns and their correlation index
    
    # The first segment adds the name of the column we are analyzing
    # The second segment adds the names of the columns correlated (except the column we are analyzing) > 0.95
    # The third segment adds the correlation index of the columns correlated (except the column we are analyzing) > 0.95
    # Second and third segment are added to the first segment as a list of lists
    
    # First we need to create a dictionary with the column names and their correlation values (except the column we are analyzing)
    dict = ({key: value for key, value in correlation[column][mask].sort_values(ascending = False).to_dict().items() if key != column})
    # print (dict)
    
    # Then we create a list of lists with the column names and their correlation values from the dictionary created above
    corr_list = [[key] + [value] for key, value in dict.items()]
    # Finally we add the name of the column we are analyzing to the list of lists created above as the first element of the list (str)
    corr_list.insert(0, f"Columna: {column}")
    
    # ! Data structure: [[columna, [columna correlada 1, indice de correlacion], [columna correlada 2, indice de correlacion], ...], ...] 
    print(corr_list)
    
    correlation_list += [corr_list]
print(correlation_list)
['Columna: apcp_sf1_1']
['Columna: apcp_sf2_1']
['Columna: apcp_sf3_1']
['Columna: apcp_sf4_1']
['Columna: apcp_sf5_1']
['Columna: dlwrf_s1_1', ['dlwrf_s2_1', 0.9650067922254768], ['dlwrf_s3_1', 0.9547817730760655]]
['Columna: dlwrf_s2_1', ['dlwrf_s3_1', 0.993701215706055], ['dlwrf_s1_1', 0.9650067922254768]]
['Columna: dlwrf_s3_1', ['dlwrf_s2_1', 0.993701215706055], ['dlwrf_s4_1', 0.9659874690575408], ['dlwrf_s5_1', 0.9552712673845433], ['dlwrf_s1_1', 0.9547817730760655]]
['Columna: dlwrf_s4_1', ['dlwrf_s5_1', 0.9969222914149775], ['dlwrf_s3_1', 0.9659874690575408]]
['Columna: dlwrf_s5_1', ['dlwrf_s4_1', 0.9969222914149775], ['dlwrf_s3_1', 0.9552712673845433]]
['Columna: dswrf_s1_1']
['Columna: dswrf_s2_1', ['uswrf_s2_1', 0.9911709851006711], ['dswrf_s3_1', 0.9503896354343679]]
['Columna: dswrf_s3_1', ['uswrf_s2_1', 0.9591814530708258], ['dswrf_s2_1', 0.9503896354343679]]
['Columna: dswrf_s4_1', ['dswrf_s5_1', 0.982758557897581]]
['Columna: dswrf_s5_1', ['dswrf_s4_1', 0.982758557897581]]
['Columna: pres_ms1_1', ['pres_ms2_1', 0.9879236602955379], ['pres_ms3_1', 0.956852960202746]]
['Columna: pres_ms2_1', ['pres_ms1_1', 0.9879236602955379], ['pres_ms3_1', 0.9869377705171734], ['pres_ms4_1', 0.9536176398645005]]
['Columna: pres_ms3_1', ['pres_ms2_1', 0.9869377705171734], ['pres_ms4_1', 0.9866602703072012], ['pres_ms1_1', 0.956852960202746], ['pres_ms5_1', 0.9538147697170144]]
['Columna: pres_ms4_1', ['pres_ms3_1', 0.9866602703072012], ['pres_ms5_1', 0.9851755074525863], ['pres_ms2_1', 0.9536176398645005]]
['Columna: pres_ms5_1', ['pres_ms4_1', 0.9851755074525863], ['pres_ms3_1', 0.9538147697170144]]
['Columna: pwat_ea1_1', ['pwat_ea2_1', 0.9859484994851248], ['pwat_ea3_1', 0.9577107162594556]]
['Columna: pwat_ea2_1', ['pwat_ea3_1', 0.9874259658433963], ['pwat_ea1_1', 0.9859484994851248], ['pwat_ea4_1', 0.9618712300670131]]
['Columna: pwat_ea3_1', ['pwat_ea4_1', 0.9880603787665849], ['pwat_ea2_1', 0.9874259658433963], ['pwat_ea5_1', 0.9616424908340101], ['pwat_ea1_1', 0.9577107162594556]]
['Columna: pwat_ea4_1', ['pwat_ea3_1', 0.9880603787665849], ['pwat_ea5_1', 0.986763801908917], ['pwat_ea2_1', 0.9618712300670131]]
['Columna: pwat_ea5_1', ['pwat_ea4_1', 0.986763801908917], ['pwat_ea3_1', 0.9616424908340101]]
['Columna: spfh_2m1_1', ['spfh_2m2_1', 0.9742691195680059]]
['Columna: spfh_2m2_1', ['spfh_2m3_1', 0.9846069576918387], ['spfh_2m1_1', 0.9742691195680059], ['spfh_2m4_1', 0.9600698332225309]]
['Columna: spfh_2m3_1', ['spfh_2m4_1', 0.9891201306737782], ['spfh_2m2_1', 0.9846069576918387], ['spfh_2m5_1', 0.9771699520274281]]
['Columna: spfh_2m4_1', ['spfh_2m5_1', 0.9904262248914517], ['spfh_2m3_1', 0.9891201306737782], ['spfh_2m2_1', 0.9600698332225309]]
['Columna: spfh_2m5_1', ['spfh_2m4_1', 0.9904262248914517], ['spfh_2m3_1', 0.9771699520274281]]
['Columna: tcdc_ea1_1', ['tcolc_e1_1', 0.9999826963362115]]
['Columna: tcdc_ea2_1', ['tcolc_e2_1', 0.9999837132775715]]
['Columna: tcdc_ea3_1', ['tcolc_e3_1', 0.9999845616560729]]
['Columna: tcdc_ea4_1', ['tcolc_e4_1', 0.999984785893167]]
['Columna: tcdc_ea5_1', ['tcolc_e5_1', 0.9999746391911669]]
['Columna: tcolc_e1_1', ['tcdc_ea1_1', 0.9999826963362115]]
['Columna: tcolc_e2_1', ['tcdc_ea2_1', 0.9999837132775715]]
['Columna: tcolc_e3_1', ['tcdc_ea3_1', 0.9999845616560729]]
['Columna: tcolc_e4_1', ['tcdc_ea4_1', 0.999984785893167]]
['Columna: tcolc_e5_1', ['tcdc_ea5_1', 0.9999746391911669]]
['Columna: tmax_2m1_1', ['ulwrf_s1_1', 0.9925465923917536], ['tmin_2m1_1', 0.9864627566914622], ['tmp_2m_1_1', 0.9844648786308661], ['tmp_sfc1_1', 0.9826171735169642], ['tmin_2m2_1', 0.9794577781348043], ['tmin_2m3_1', 0.97879484323375], ['ulwrf_s2_1', 0.9707221719806952], ['tmax_2m2_1', 0.9637997824764319], ['tmp_2m_2_1', 0.9602996922677912], ['ulwrf_s3_1', 0.9578768560091268], ['tmp_sfc2_1', 0.9528200105400535]]
['Columna: tmax_2m2_1', ['tmp_2m_2_1', 0.9993112900738094], ['tmp_sfc2_1', 0.9963595768447152], ['ulwrf_s3_1', 0.9943559569788851], ['ulwrf_s2_1', 0.9917542607726626], ['tmax_2m3_1', 0.9863610206089146], ['tmp_2m_3_1', 0.9829472636912582], ['tmin_2m2_1', 0.9819461458841241], ['tmin_2m3_1', 0.9819334574863472], ['tmin_2m4_1', 0.9790285687297058], ['tmp_2m_1_1', 0.9771397511742945], ['tmin_2m1_1', 0.9735093237780129], ['tmin_2m5_1', 0.9713195080332866], ['tmax_2m4_1', 0.9698857690834339], ['tmax_2m5_1', 0.9697541323437304], ['tmp_sfc1_1', 0.9697293778574791], ['tmp_sfc5_1', 0.9692885564165558], ['tmp_2m_5_1', 0.9675902215544175], ['tmp_2m_4_1', 0.9645870257681579], ['tmax_2m1_1', 0.9637997824764319], ['ulwrf_s1_1', 0.9606784450210313], ['ulwrf_s5_1', 0.9582268665523904], ['tmp_sfc3_1', 0.9540154794130064]]
['Columna: tmax_2m3_1', ['tmp_2m_3_1', 0.9989979986044517], ['tmin_2m4_1', 0.9973034556239585], ['tmax_2m4_1', 0.9937711137699543], ['tmax_2m5_1', 0.9931925682521422], ['tmp_2m_4_1', 0.9902875444682745], ['ulwrf_s3_1', 0.9882838798756105], ['tmp_2m_2_1', 0.9880399268817291], ['tmp_sfc2_1', 0.9874628996347063], ['tmax_2m2_1', 0.9863610206089146], ['tmin_2m5_1', 0.9849440628695366], ['tmp_sfc3_1', 0.9836268315982332], ['ulwrf_s5_1', 0.9831073628529786], ['tmp_2m_5_1', 0.9800734262132967], ['ulwrf_s4_1', 0.9784038012441758], ['tmp_sfc4_1', 0.977121003001589], ['tmp_sfc5_1', 0.9751782371847001], ['ulwrf_s2_1', 0.966905126635995], ['tmin_2m3_1', 0.9565532246066281], ['tmin_2m2_1', 0.9554925734198499]]
['Columna: tmax_2m4_1', ['tmax_2m5_1', 0.999855391919824], ['tmp_2m_4_1', 0.9989670084606509], ['tmin_2m4_1', 0.9965267117336937], ['tmp_2m_3_1', 0.9954824569443925], ['tmax_2m3_1', 0.9937711137699543], ['ulwrf_s5_1', 0.9915793553887863], ['tmp_sfc4_1', 0.9903005164322048], ['tmin_2m5_1', 0.9888950622930037], ['ulwrf_s4_1', 0.987077087459209], ['tmp_2m_5_1', 0.9862698111992504], ['tmp_sfc3_1', 0.9857825429301692], ['tmp_sfc5_1', 0.9780961580272722], ['ulwrf_s3_1', 0.975826585247475], ['tmp_sfc2_1', 0.9734162968894661], ['tmp_2m_2_1', 0.9730783300205592], ['tmax_2m2_1', 0.9698857690834339]]
['Columna: tmax_2m5_1', ['tmax_2m4_1', 0.999855391919824], ['tmp_2m_4_1', 0.9988753498975144], ['tmin_2m4_1', 0.9959215026917639], ['tmp_2m_3_1', 0.9948623637802105], ['tmax_2m3_1', 0.9931925682521422], ['ulwrf_s5_1', 0.99151293872598], ['tmp_sfc4_1', 0.9902303273948138], ['tmin_2m5_1', 0.9891405894645761], ['tmp_2m_5_1', 0.9872536923433799], ['ulwrf_s4_1', 0.9863521279974694], ['tmp_sfc3_1', 0.9848432369308402], ['tmp_sfc5_1', 0.9791492889290042], ['ulwrf_s3_1', 0.975536953838263], ['tmp_sfc2_1', 0.9732760733014082], ['tmp_2m_2_1', 0.9729567511523166], ['tmax_2m2_1', 0.9697541323437304]]
['Columna: tmin_2m1_1', ['tmp_2m_1_1', 0.9981185076252812], ['tmp_sfc1_1', 0.9963142972792025], ['tmin_2m2_1', 0.9950949108277914], ['tmin_2m3_1', 0.9943408586923532], ['ulwrf_s1_1', 0.9926165091998508], ['tmax_2m1_1', 0.9864627566914622], ['ulwrf_s2_1', 0.9814254257054185], ['tmax_2m2_1', 0.9735093237780129], ['tmp_2m_2_1', 0.9708467193246784], ['ulwrf_s3_1', 0.9654648681213764], ['tmp_sfc2_1', 0.9605896048258724]]
['Columna: tmin_2m2_1', ['tmin_2m3_1', 0.9996572623026859], ['tmp_2m_1_1', 0.9981819106379802], ['tmp_sfc1_1', 0.9960749292152973], ['tmin_2m1_1', 0.9950949108277914], ['ulwrf_s2_1', 0.9899721168841563], ['ulwrf_s1_1', 0.9850580289147287], ['tmax_2m2_1', 0.9819461458841241], ['tmp_2m_2_1', 0.9808603480091717], ['tmax_2m1_1', 0.9794577781348043], ['ulwrf_s3_1', 0.9743529570168544], ['tmp_sfc2_1', 0.9709866438853475], ['tmax_2m3_1', 0.9554925734198499], ['tmp_2m_3_1', 0.9516543862813964]]
['Columna: tmin_2m3_1', ['tmin_2m2_1', 0.9996572623026859], ['tmp_2m_1_1', 0.9973859703817012], ['tmp_sfc1_1', 0.9951903927420194], ['tmin_2m1_1', 0.9943408586923532], ['ulwrf_s2_1', 0.9897318251363909], ['ulwrf_s1_1', 0.9843176374301973], ['tmax_2m2_1', 0.9819334574863472], ['tmp_2m_2_1', 0.9813049765366397], ['tmax_2m1_1', 0.97879484323375], ['ulwrf_s3_1', 0.9751256747221002], ['tmp_sfc2_1', 0.9715874768684567], ['tmax_2m3_1', 0.9565532246066281], ['tmp_2m_3_1', 0.9537926818714694]]
['Columna: tmin_2m4_1', ['tmp_2m_3_1', 0.9989480053798309], ['tmax_2m3_1', 0.9973034556239585], ['tmax_2m4_1', 0.9965267117336937], ['tmax_2m5_1', 0.9959215026917639], ['tmp_2m_4_1', 0.9955546180266533], ['tmin_2m5_1', 0.9884708317878447], ['ulwrf_s5_1', 0.9881522932211056], ['tmp_sfc3_1', 0.985897294709102], ['tmp_sfc4_1', 0.9839686317112281], ['ulwrf_s4_1', 0.9837254094808376], ['tmp_2m_5_1', 0.9836800034039297], ['ulwrf_s3_1', 0.9834305304179148], ['tmp_2m_2_1', 0.9819192741530762], ['tmp_sfc2_1', 0.9818609853360799], ['tmax_2m2_1', 0.9790285687297058], ['tmp_sfc5_1', 0.9773521584222015], ['ulwrf_s2_1', 0.9587402415390521]]
['Columna: tmin_2m5_1', ['tmp_2m_5_1', 0.9985248666465218], ['tmp_sfc5_1', 0.9960054258735697], ['tmp_2m_4_1', 0.9895327574093381], ['tmax_2m5_1', 0.9891405894645761], ['tmax_2m4_1', 0.9888950622930037], ['tmin_2m4_1', 0.9884708317878447], ['ulwrf_s5_1', 0.9873222874147335], ['tmp_2m_3_1', 0.9863630955598195], ['tmax_2m3_1', 0.9849440628695366], ['tmp_sfc4_1', 0.9799245981499726], ['ulwrf_s3_1', 0.9771636437810954], ['tmp_sfc2_1', 0.975307217691161], ['tmp_2m_2_1', 0.973997775172227], ['ulwrf_s4_1', 0.9737488476761204], ['tmax_2m2_1', 0.9713195080332866], ['tmp_sfc3_1', 0.9704219757785946], ['ulwrf_s2_1', 0.9584808725553905]]
['Columna: tmp_2m_1_1', ['tmin_2m2_1', 0.9981819106379802], ['tmin_2m1_1', 0.9981185076252812], ['tmp_sfc1_1', 0.9979448017549044], ['tmin_2m3_1', 0.9973859703817012], ['ulwrf_s1_1', 0.9897625110599417], ['ulwrf_s2_1', 0.9853437253651708], ['tmax_2m1_1', 0.9844648786308661], ['tmax_2m2_1', 0.9771397511742945], ['tmp_2m_2_1', 0.9744909003873826], ['ulwrf_s3_1', 0.968308266178652], ['tmp_sfc2_1', 0.9638593940360212]]
['Columna: tmp_2m_2_1', ['tmax_2m2_1', 0.9993112900738094], ['tmp_sfc2_1', 0.9971658992806404], ['ulwrf_s3_1', 0.994870585784455], ['ulwrf_s2_1', 0.990609269111517], ['tmax_2m3_1', 0.9880399268817291], ['tmp_2m_3_1', 0.9856921834337115], ['tmin_2m4_1', 0.9819192741530762], ['tmin_2m3_1', 0.9813049765366397], ['tmin_2m2_1', 0.9808603480091717], ['tmp_2m_1_1', 0.9744909003873826], ['tmin_2m5_1', 0.973997775172227], ['tmax_2m4_1', 0.9730783300205592], ['tmax_2m5_1', 0.9729567511523166], ['tmp_sfc5_1', 0.9714528776518785], ['tmin_2m1_1', 0.9708467193246784], ['tmp_2m_5_1', 0.9702697100229983], ['tmp_2m_4_1', 0.9679046544965666], ['tmp_sfc1_1', 0.9668200402557023], ['ulwrf_s5_1', 0.960980140611558], ['tmax_2m1_1', 0.9602996922677912], ['ulwrf_s1_1', 0.9573813147342563], ['tmp_sfc3_1', 0.9570765900532514]]
['Columna: tmp_2m_3_1', ['tmax_2m3_1', 0.9989979986044517], ['tmin_2m4_1', 0.9989480053798309], ['tmax_2m4_1', 0.9954824569443925], ['tmax_2m5_1', 0.9948623637802105], ['tmp_2m_4_1', 0.9925508354894933], ['ulwrf_s3_1', 0.986475159576972], ['tmin_2m5_1', 0.9863630955598195], ['tmp_2m_2_1', 0.9856921834337115], ['tmp_sfc3_1', 0.9856020769129077], ['tmp_sfc2_1', 0.9853721430018374], ['ulwrf_s5_1', 0.9850287211532148], ['tmax_2m2_1', 0.9829472636912582], ['tmp_2m_5_1', 0.9813875596975576], ['ulwrf_s4_1', 0.9807390701133252], ['tmp_sfc4_1', 0.9796642142509698], ['tmp_sfc5_1', 0.9758811197330793], ['ulwrf_s2_1', 0.9631310421561378], ['tmin_2m3_1', 0.9537926818714694], ['tmin_2m2_1', 0.9516543862813964]]
['Columna: tmp_2m_4_1', ['tmax_2m4_1', 0.9989670084606509], ['tmax_2m5_1', 0.9988753498975144], ['tmin_2m4_1', 0.9955546180266533], ['ulwrf_s5_1', 0.9926662202081515], ['tmp_2m_3_1', 0.9925508354894933], ['tmp_sfc4_1', 0.9924835965861123], ['tmax_2m3_1', 0.9902875444682745], ['tmin_2m5_1', 0.9895327574093381], ['ulwrf_s4_1', 0.9875947598774877], ['tmp_2m_5_1', 0.9871404965220815], ['tmp_sfc3_1', 0.9838690005793208], ['tmp_sfc5_1', 0.9781934487046426], ['ulwrf_s3_1', 0.9712226930987012], ['tmp_sfc2_1', 0.9684774894714101], ['tmp_2m_2_1', 0.9679046544965666], ['tmax_2m2_1', 0.9645870257681579]]
['Columna: tmp_2m_5_1', ['tmin_2m5_1', 0.9985248666465218], ['tmp_sfc5_1', 0.9980075740584928], ['tmax_2m5_1', 0.9872536923433799], ['tmp_2m_4_1', 0.9871404965220815], ['tmax_2m4_1', 0.9862698111992504], ['ulwrf_s5_1', 0.9852702329370912], ['tmin_2m4_1', 0.9836800034039297], ['tmp_2m_3_1', 0.9813875596975576], ['tmax_2m3_1', 0.9800734262132967], ['tmp_sfc4_1', 0.9781233238955636], ['ulwrf_s3_1', 0.9731828651939985], ['tmp_sfc2_1', 0.971798288488127], ['tmp_2m_2_1', 0.9702697100229983], ['ulwrf_s4_1', 0.9695091232286572], ['tmax_2m2_1', 0.9675902215544175], ['tmp_sfc3_1', 0.9646544198978636], ['ulwrf_s2_1', 0.9560882131646383]]
['Columna: tmp_sfc1_1', ['tmp_2m_1_1', 0.9979448017549044], ['tmin_2m1_1', 0.9963142972792025], ['tmin_2m2_1', 0.9960749292152973], ['tmin_2m3_1', 0.9951903927420194], ['ulwrf_s1_1', 0.9919281097281679], ['ulwrf_s2_1', 0.9842676480547997], ['tmax_2m1_1', 0.9826171735169642], ['tmax_2m2_1', 0.9697293778574791], ['tmp_2m_2_1', 0.9668200402557023], ['ulwrf_s3_1', 0.9621315029521358], ['tmp_sfc2_1', 0.957188784436685]]
['Columna: tmp_sfc2_1', ['tmp_2m_2_1', 0.9971658992806404], ['ulwrf_s3_1', 0.996855293888584], ['tmax_2m2_1', 0.9963595768447152], ['ulwrf_s2_1', 0.9879322271553737], ['tmax_2m3_1', 0.9874628996347063], ['tmp_2m_3_1', 0.9853721430018374], ['tmin_2m4_1', 0.9818609853360799], ['tmin_2m5_1', 0.975307217691161], ['tmp_sfc5_1', 0.9740593607013978], ['tmax_2m4_1', 0.9734162968894661], ['tmax_2m5_1', 0.9732760733014082], ['tmp_2m_5_1', 0.971798288488127], ['tmin_2m3_1', 0.9715874768684567], ['tmin_2m2_1', 0.9709866438853475], ['tmp_2m_4_1', 0.9684774894714101], ['ulwrf_s5_1', 0.9670339151339817], ['tmp_sfc3_1', 0.9649823936827109], ['tmp_2m_1_1', 0.9638593940360212], ['tmin_2m1_1', 0.9605896048258724], ['ulwrf_s4_1', 0.9572236269499521], ['tmp_sfc1_1', 0.957188784436685], ['tmp_sfc4_1', 0.9555363809053586], ['tmax_2m1_1', 0.9528200105400535]]
['Columna: tmp_sfc3_1', ['ulwrf_s4_1', 0.9947627885687921], ['ulwrf_s5_1', 0.9892581590922543], ['tmp_sfc4_1', 0.9884745475700606], ['tmin_2m4_1', 0.985897294709102], ['tmax_2m4_1', 0.9857825429301692], ['tmp_2m_3_1', 0.9856020769129077], ['tmax_2m5_1', 0.9848432369308402], ['tmp_2m_4_1', 0.9838690005793208], ['tmax_2m3_1', 0.9836268315982332], ['tmin_2m5_1', 0.9704219757785946], ['ulwrf_s3_1', 0.9698096931439735], ['tmp_sfc2_1', 0.9649823936827109], ['tmp_2m_5_1', 0.9646544198978636], ['tmp_2m_2_1', 0.9570765900532514], ['tmp_sfc5_1', 0.9562755066656142], ['tmax_2m2_1', 0.9540154794130064]]
['Columna: tmp_sfc4_1', ['ulwrf_s5_1', 0.996612200039398], ['ulwrf_s4_1', 0.9957411309514121], ['tmp_2m_4_1', 0.9924835965861123], ['tmax_2m4_1', 0.9903005164322048], ['tmax_2m5_1', 0.9902303273948138], ['tmp_sfc3_1', 0.9884745475700606], ['tmin_2m4_1', 0.9839686317112281], ['tmin_2m5_1', 0.9799245981499726], ['tmp_2m_3_1', 0.9796642142509698], ['tmp_2m_5_1', 0.9781233238955636], ['tmax_2m3_1', 0.977121003001589], ['tmp_sfc5_1', 0.9687614236330414], ['ulwrf_s3_1', 0.9604279752910915], ['tmp_sfc2_1', 0.9555363809053586]]
['Columna: tmp_sfc5_1', ['tmp_2m_5_1', 0.9980075740584928], ['tmin_2m5_1', 0.9960054258735697], ['tmax_2m5_1', 0.9791492889290042], ['ulwrf_s5_1', 0.9789322162596626], ['tmp_2m_4_1', 0.9781934487046426], ['tmax_2m4_1', 0.9780961580272722], ['tmin_2m4_1', 0.9773521584222015], ['tmp_2m_3_1', 0.9758811197330793], ['tmax_2m3_1', 0.9751782371847001], ['ulwrf_s3_1', 0.9744478191517459], ['tmp_sfc2_1', 0.9740593607013978], ['tmp_2m_2_1', 0.9714528776518785], ['tmax_2m2_1', 0.9692885564165558], ['tmp_sfc4_1', 0.9687614236330414], ['ulwrf_s2_1', 0.9619766387479004], ['ulwrf_s4_1', 0.960457161005563], ['tmp_sfc3_1', 0.9562755066656142]]
['Columna: ulwrf_s1_1', ['tmin_2m1_1', 0.9926165091998508], ['tmax_2m1_1', 0.9925465923917536], ['tmp_sfc1_1', 0.9919281097281679], ['tmp_2m_1_1', 0.9897625110599417], ['tmin_2m2_1', 0.9850580289147287], ['tmin_2m3_1', 0.9843176374301973], ['ulwrf_s2_1', 0.9762674995860944], ['tmax_2m2_1', 0.9606784450210313], ['ulwrf_s3_1', 0.9574576992187499], ['tmp_2m_2_1', 0.9573813147342563]]
['Columna: ulwrf_s2_1', ['tmax_2m2_1', 0.9917542607726626], ['tmp_2m_2_1', 0.990609269111517], ['ulwrf_s3_1', 0.990564307766117], ['tmin_2m2_1', 0.9899721168841563], ['tmin_2m3_1', 0.9897318251363909], ['tmp_sfc2_1', 0.9879322271553737], ['tmp_2m_1_1', 0.9853437253651708], ['tmp_sfc1_1', 0.9842676480547997], ['tmin_2m1_1', 0.9814254257054185], ['ulwrf_s1_1', 0.9762674995860944], ['tmax_2m1_1', 0.9707221719806952], ['tmax_2m3_1', 0.966905126635995], ['tmp_2m_3_1', 0.9631310421561378], ['tmp_sfc5_1', 0.9619766387479004], ['tmin_2m4_1', 0.9587402415390521], ['tmin_2m5_1', 0.9584808725553905], ['tmp_2m_5_1', 0.9560882131646383]]
['Columna: ulwrf_s3_1', ['tmp_sfc2_1', 0.996855293888584], ['tmp_2m_2_1', 0.994870585784455], ['tmax_2m2_1', 0.9943559569788851], ['ulwrf_s2_1', 0.990564307766117], ['tmax_2m3_1', 0.9882838798756105], ['tmp_2m_3_1', 0.986475159576972], ['tmin_2m4_1', 0.9834305304179148], ['tmin_2m5_1', 0.9771636437810954], ['tmax_2m4_1', 0.975826585247475], ['tmax_2m5_1', 0.975536953838263], ['tmin_2m3_1', 0.9751256747221002], ['tmp_sfc5_1', 0.9744478191517459], ['tmin_2m2_1', 0.9743529570168544], ['ulwrf_s5_1', 0.9734148064192735], ['tmp_2m_5_1', 0.9731828651939985], ['tmp_2m_4_1', 0.9712226930987012], ['tmp_sfc3_1', 0.9698096931439735], ['tmp_2m_1_1', 0.968308266178652], ['tmin_2m1_1', 0.9654648681213764], ['ulwrf_s4_1', 0.9651706956885256], ['tmp_sfc1_1', 0.9621315029521358], ['tmp_sfc4_1', 0.9604279752910915], ['tmax_2m1_1', 0.9578768560091268], ['ulwrf_s1_1', 0.9574576992187499]]
['Columna: ulwrf_s4_1', ['ulwrf_s5_1', 0.9963430558611763], ['tmp_sfc4_1', 0.9957411309514121], ['tmp_sfc3_1', 0.9947627885687921], ['tmp_2m_4_1', 0.9875947598774877], ['tmax_2m4_1', 0.987077087459209], ['tmax_2m5_1', 0.9863521279974694], ['tmin_2m4_1', 0.9837254094808376], ['tmp_2m_3_1', 0.9807390701133252], ['tmax_2m3_1', 0.9784038012441758], ['tmin_2m5_1', 0.9737488476761204], ['tmp_2m_5_1', 0.9695091232286572], ['ulwrf_s3_1', 0.9651706956885256], ['tmp_sfc5_1', 0.960457161005563], ['tmp_sfc2_1', 0.9572236269499521]]
['Columna: ulwrf_s5_1', ['tmp_sfc4_1', 0.996612200039398], ['ulwrf_s4_1', 0.9963430558611763], ['tmp_2m_4_1', 0.9926662202081515], ['tmax_2m4_1', 0.9915793553887863], ['tmax_2m5_1', 0.99151293872598], ['tmp_sfc3_1', 0.9892581590922543], ['tmin_2m4_1', 0.9881522932211056], ['tmin_2m5_1', 0.9873222874147335], ['tmp_2m_5_1', 0.9852702329370912], ['tmp_2m_3_1', 0.9850287211532148], ['tmax_2m3_1', 0.9831073628529786], ['tmp_sfc5_1', 0.9789322162596626], ['ulwrf_s3_1', 0.9734148064192735], ['tmp_sfc2_1', 0.9670339151339817], ['tmp_2m_2_1', 0.960980140611558], ['tmax_2m2_1', 0.9582268665523904]]
['Columna: ulwrf_t1_1']
['Columna: ulwrf_t2_1', ['ulwrf_t3_1', 0.9744666921198298]]
['Columna: ulwrf_t3_1', ['ulwrf_t2_1', 0.9744666921198298]]
['Columna: ulwrf_t4_1', ['ulwrf_t5_1', 0.9755542908956468]]
['Columna: ulwrf_t5_1', ['ulwrf_t4_1', 0.9755542908956468]]
['Columna: uswrf_s1_1']
['Columna: uswrf_s2_1', ['dswrf_s2_1', 0.9911709851006711], ['dswrf_s3_1', 0.9591814530708258]]
['Columna: uswrf_s3_1']
['Columna: uswrf_s4_1', ['uswrf_s5_1', 0.9562280634672189]]
['Columna: uswrf_s5_1', ['uswrf_s4_1', 0.9562280634672189]]
['Columna: salida']
[['Columna: apcp_sf1_1'], ['Columna: apcp_sf2_1'], ['Columna: apcp_sf3_1'], ['Columna: apcp_sf4_1'], ['Columna: apcp_sf5_1'], ['Columna: dlwrf_s1_1', ['dlwrf_s2_1', 0.9650067922254768], ['dlwrf_s3_1', 0.9547817730760655]], ['Columna: dlwrf_s2_1', ['dlwrf_s3_1', 0.993701215706055], ['dlwrf_s1_1', 0.9650067922254768]], ['Columna: dlwrf_s3_1', ['dlwrf_s2_1', 0.993701215706055], ['dlwrf_s4_1', 0.9659874690575408], ['dlwrf_s5_1', 0.9552712673845433], ['dlwrf_s1_1', 0.9547817730760655]], ['Columna: dlwrf_s4_1', ['dlwrf_s5_1', 0.9969222914149775], ['dlwrf_s3_1', 0.9659874690575408]], ['Columna: dlwrf_s5_1', ['dlwrf_s4_1', 0.9969222914149775], ['dlwrf_s3_1', 0.9552712673845433]], ['Columna: dswrf_s1_1'], ['Columna: dswrf_s2_1', ['uswrf_s2_1', 0.9911709851006711], ['dswrf_s3_1', 0.9503896354343679]], ['Columna: dswrf_s3_1', ['uswrf_s2_1', 0.9591814530708258], ['dswrf_s2_1', 0.9503896354343679]], ['Columna: dswrf_s4_1', ['dswrf_s5_1', 0.982758557897581]], ['Columna: dswrf_s5_1', ['dswrf_s4_1', 0.982758557897581]], ['Columna: pres_ms1_1', ['pres_ms2_1', 0.9879236602955379], ['pres_ms3_1', 0.956852960202746]], ['Columna: pres_ms2_1', ['pres_ms1_1', 0.9879236602955379], ['pres_ms3_1', 0.9869377705171734], ['pres_ms4_1', 0.9536176398645005]], ['Columna: pres_ms3_1', ['pres_ms2_1', 0.9869377705171734], ['pres_ms4_1', 0.9866602703072012], ['pres_ms1_1', 0.956852960202746], ['pres_ms5_1', 0.9538147697170144]], ['Columna: pres_ms4_1', ['pres_ms3_1', 0.9866602703072012], ['pres_ms5_1', 0.9851755074525863], ['pres_ms2_1', 0.9536176398645005]], ['Columna: pres_ms5_1', ['pres_ms4_1', 0.9851755074525863], ['pres_ms3_1', 0.9538147697170144]], ['Columna: pwat_ea1_1', ['pwat_ea2_1', 0.9859484994851248], ['pwat_ea3_1', 0.9577107162594556]], ['Columna: pwat_ea2_1', ['pwat_ea3_1', 0.9874259658433963], ['pwat_ea1_1', 0.9859484994851248], ['pwat_ea4_1', 0.9618712300670131]], ['Columna: pwat_ea3_1', ['pwat_ea4_1', 0.9880603787665849], ['pwat_ea2_1', 0.9874259658433963], ['pwat_ea5_1', 0.9616424908340101], ['pwat_ea1_1', 0.9577107162594556]], ['Columna: pwat_ea4_1', ['pwat_ea3_1', 0.9880603787665849], ['pwat_ea5_1', 0.986763801908917], ['pwat_ea2_1', 0.9618712300670131]], ['Columna: pwat_ea5_1', ['pwat_ea4_1', 0.986763801908917], ['pwat_ea3_1', 0.9616424908340101]], ['Columna: spfh_2m1_1', ['spfh_2m2_1', 0.9742691195680059]], ['Columna: spfh_2m2_1', ['spfh_2m3_1', 0.9846069576918387], ['spfh_2m1_1', 0.9742691195680059], ['spfh_2m4_1', 0.9600698332225309]], ['Columna: spfh_2m3_1', ['spfh_2m4_1', 0.9891201306737782], ['spfh_2m2_1', 0.9846069576918387], ['spfh_2m5_1', 0.9771699520274281]], ['Columna: spfh_2m4_1', ['spfh_2m5_1', 0.9904262248914517], ['spfh_2m3_1', 0.9891201306737782], ['spfh_2m2_1', 0.9600698332225309]], ['Columna: spfh_2m5_1', ['spfh_2m4_1', 0.9904262248914517], ['spfh_2m3_1', 0.9771699520274281]], ['Columna: tcdc_ea1_1', ['tcolc_e1_1', 0.9999826963362115]], ['Columna: tcdc_ea2_1', ['tcolc_e2_1', 0.9999837132775715]], ['Columna: tcdc_ea3_1', ['tcolc_e3_1', 0.9999845616560729]], ['Columna: tcdc_ea4_1', ['tcolc_e4_1', 0.999984785893167]], ['Columna: tcdc_ea5_1', ['tcolc_e5_1', 0.9999746391911669]], ['Columna: tcolc_e1_1', ['tcdc_ea1_1', 0.9999826963362115]], ['Columna: tcolc_e2_1', ['tcdc_ea2_1', 0.9999837132775715]], ['Columna: tcolc_e3_1', ['tcdc_ea3_1', 0.9999845616560729]], ['Columna: tcolc_e4_1', ['tcdc_ea4_1', 0.999984785893167]], ['Columna: tcolc_e5_1', ['tcdc_ea5_1', 0.9999746391911669]], ['Columna: tmax_2m1_1', ['ulwrf_s1_1', 0.9925465923917536], ['tmin_2m1_1', 0.9864627566914622], ['tmp_2m_1_1', 0.9844648786308661], ['tmp_sfc1_1', 0.9826171735169642], ['tmin_2m2_1', 0.9794577781348043], ['tmin_2m3_1', 0.97879484323375], ['ulwrf_s2_1', 0.9707221719806952], ['tmax_2m2_1', 0.9637997824764319], ['tmp_2m_2_1', 0.9602996922677912], ['ulwrf_s3_1', 0.9578768560091268], ['tmp_sfc2_1', 0.9528200105400535]], ['Columna: tmax_2m2_1', ['tmp_2m_2_1', 0.9993112900738094], ['tmp_sfc2_1', 0.9963595768447152], ['ulwrf_s3_1', 0.9943559569788851], ['ulwrf_s2_1', 0.9917542607726626], ['tmax_2m3_1', 0.9863610206089146], ['tmp_2m_3_1', 0.9829472636912582], ['tmin_2m2_1', 0.9819461458841241], ['tmin_2m3_1', 0.9819334574863472], ['tmin_2m4_1', 0.9790285687297058], ['tmp_2m_1_1', 0.9771397511742945], ['tmin_2m1_1', 0.9735093237780129], ['tmin_2m5_1', 0.9713195080332866], ['tmax_2m4_1', 0.9698857690834339], ['tmax_2m5_1', 0.9697541323437304], ['tmp_sfc1_1', 0.9697293778574791], ['tmp_sfc5_1', 0.9692885564165558], ['tmp_2m_5_1', 0.9675902215544175], ['tmp_2m_4_1', 0.9645870257681579], ['tmax_2m1_1', 0.9637997824764319], ['ulwrf_s1_1', 0.9606784450210313], ['ulwrf_s5_1', 0.9582268665523904], ['tmp_sfc3_1', 0.9540154794130064]], ['Columna: tmax_2m3_1', ['tmp_2m_3_1', 0.9989979986044517], ['tmin_2m4_1', 0.9973034556239585], ['tmax_2m4_1', 0.9937711137699543], ['tmax_2m5_1', 0.9931925682521422], ['tmp_2m_4_1', 0.9902875444682745], ['ulwrf_s3_1', 0.9882838798756105], ['tmp_2m_2_1', 0.9880399268817291], ['tmp_sfc2_1', 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0.9573813147342563]], ['Columna: ulwrf_s2_1', ['tmax_2m2_1', 0.9917542607726626], ['tmp_2m_2_1', 0.990609269111517], ['ulwrf_s3_1', 0.990564307766117], ['tmin_2m2_1', 0.9899721168841563], ['tmin_2m3_1', 0.9897318251363909], ['tmp_sfc2_1', 0.9879322271553737], ['tmp_2m_1_1', 0.9853437253651708], ['tmp_sfc1_1', 0.9842676480547997], ['tmin_2m1_1', 0.9814254257054185], ['ulwrf_s1_1', 0.9762674995860944], ['tmax_2m1_1', 0.9707221719806952], ['tmax_2m3_1', 0.966905126635995], ['tmp_2m_3_1', 0.9631310421561378], ['tmp_sfc5_1', 0.9619766387479004], ['tmin_2m4_1', 0.9587402415390521], ['tmin_2m5_1', 0.9584808725553905], ['tmp_2m_5_1', 0.9560882131646383]], ['Columna: ulwrf_s3_1', ['tmp_sfc2_1', 0.996855293888584], ['tmp_2m_2_1', 0.994870585784455], ['tmax_2m2_1', 0.9943559569788851], ['ulwrf_s2_1', 0.990564307766117], ['tmax_2m3_1', 0.9882838798756105], ['tmp_2m_3_1', 0.986475159576972], ['tmin_2m4_1', 0.9834305304179148], ['tmin_2m5_1', 0.9771636437810954], ['tmax_2m4_1', 0.975826585247475], ['tmax_2m5_1', 0.975536953838263], ['tmin_2m3_1', 0.9751256747221002], ['tmp_sfc5_1', 0.9744478191517459], ['tmin_2m2_1', 0.9743529570168544], ['ulwrf_s5_1', 0.9734148064192735], ['tmp_2m_5_1', 0.9731828651939985], ['tmp_2m_4_1', 0.9712226930987012], ['tmp_sfc3_1', 0.9698096931439735], ['tmp_2m_1_1', 0.968308266178652], ['tmin_2m1_1', 0.9654648681213764], ['ulwrf_s4_1', 0.9651706956885256], ['tmp_sfc1_1', 0.9621315029521358], ['tmp_sfc4_1', 0.9604279752910915], ['tmax_2m1_1', 0.9578768560091268], ['ulwrf_s1_1', 0.9574576992187499]], ['Columna: ulwrf_s4_1', ['ulwrf_s5_1', 0.9963430558611763], ['tmp_sfc4_1', 0.9957411309514121], ['tmp_sfc3_1', 0.9947627885687921], ['tmp_2m_4_1', 0.9875947598774877], ['tmax_2m4_1', 0.987077087459209], ['tmax_2m5_1', 0.9863521279974694], ['tmin_2m4_1', 0.9837254094808376], ['tmp_2m_3_1', 0.9807390701133252], ['tmax_2m3_1', 0.9784038012441758], ['tmin_2m5_1', 0.9737488476761204], ['tmp_2m_5_1', 0.9695091232286572], ['ulwrf_s3_1', 0.9651706956885256], ['tmp_sfc5_1', 0.960457161005563], ['tmp_sfc2_1', 0.9572236269499521]], ['Columna: ulwrf_s5_1', ['tmp_sfc4_1', 0.996612200039398], ['ulwrf_s4_1', 0.9963430558611763], ['tmp_2m_4_1', 0.9926662202081515], ['tmax_2m4_1', 0.9915793553887863], ['tmax_2m5_1', 0.99151293872598], ['tmp_sfc3_1', 0.9892581590922543], ['tmin_2m4_1', 0.9881522932211056], ['tmin_2m5_1', 0.9873222874147335], ['tmp_2m_5_1', 0.9852702329370912], ['tmp_2m_3_1', 0.9850287211532148], ['tmax_2m3_1', 0.9831073628529786], ['tmp_sfc5_1', 0.9789322162596626], ['ulwrf_s3_1', 0.9734148064192735], ['tmp_sfc2_1', 0.9670339151339817], ['tmp_2m_2_1', 0.960980140611558], ['tmax_2m2_1', 0.9582268665523904]], ['Columna: ulwrf_t1_1'], ['Columna: ulwrf_t2_1', ['ulwrf_t3_1', 0.9744666921198298]], ['Columna: ulwrf_t3_1', ['ulwrf_t2_1', 0.9744666921198298]], ['Columna: ulwrf_t4_1', ['ulwrf_t5_1', 0.9755542908956468]], ['Columna: ulwrf_t5_1', ['ulwrf_t4_1', 0.9755542908956468]], ['Columna: uswrf_s1_1'], ['Columna: uswrf_s2_1', ['dswrf_s2_1', 0.9911709851006711], ['dswrf_s3_1', 0.9591814530708258]], ['Columna: uswrf_s3_1'], ['Columna: uswrf_s4_1', ['uswrf_s5_1', 0.9562280634672189]], ['Columna: uswrf_s5_1', ['uswrf_s4_1', 0.9562280634672189]], ['Columna: salida']]

Correlation Heat Map¶

In [30]:
""" seaborne Correlation Heat Map """

# It needs to show all the columns
fig, ax = plt.subplots(figsize=(19,18))

plt.title('Correlation Heat Map',y=1)
# We use blue color scale because it is easier to see the annotations and the correlation values
sns.heatmap(correlation, square=True, cmap='Blues', annot=True, fmt='.2f', annot_kws={'size': 4}, linewidths=.3, cbar_kws={"shrink": .5}, vmin=0.0, vmax=1)
# We can modify vmax=0.95 in order to get same color scale for values with more than 0.95 correlation
# Note: it delays around 15 seconds as it needs to plot a 76*76 matrix with its 5766 correlation values

# Exporting image as png to ../data/img folder - easier to visualize the annotations, better resolution
plt.savefig("../data/img/correlation_heatmap.png", dpi=200)

Once obtained the most correlated columns of the dataset, we can plot them and visualize their correlation.

In [31]:
# 1
sns.set(), sns.set(font_scale=.75)
columns = ['apcp_sf1_1', 'apcp_sf2_1', 'apcp_sf3_1','apcp_sf4_1', 'apcp_sf5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [32]:
# 2

sns.set(), sns.set(font_scale=.75)
columns = [ 'dlwrf_s1_1', 'dlwrf_s2_1', 'dlwrf_s3_1', 'dlwrf_s4_1', 'dlwrf_s5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [33]:
# 3

sns.set(), sns.set(font_scale=.75)
columns = ['pwat_ea1_1', 'pwat_ea2_1','pwat_ea3_1','pwat_ea4_1','pwat_ea5_1', 'dlwrf_s1_1', 'dlwrf_s2_1', 'dlwrf_s3_1', 'dlwrf_s4_1', 'dlwrf_s5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [34]:
# 4

sns.set(), sns.set(font_scale=.75)
columns = ['dswrf_s1_1', 'dswrf_s2_1', 'dswrf_s3_1', 'dswrf_s4_1', 'dswrf_s5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [35]:
# 5

sns.set(), sns.set(font_scale=.75)
columns = ['dswrf_s1_1', 'dswrf_s2_1', 'dswrf_s3_1', 'dswrf_s4_1', 'dswrf_s5_1', 'uswrf_s1_1', 'uswrf_s2_1', 'uswrf_s3_1', 'uswrf_s4_1', 'uswrf_s5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [36]:
# 6

sns.set(), sns.set(font_scale=.75)
columns = ['pres_ms1_1', 'pres_ms2_1', 'pres_ms3_1', 'pres_ms4_1', 'pres_ms5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [37]:
# 7

sns.set(), sns.set(font_scale=.75)
columns = ['pwat_ea1_1', 'pwat_ea2_1','pwat_ea3_1','pwat_ea4_1','pwat_ea5_1', 'spfh_2m1_1', 'spfh_2m2_1', 'spfh_2m3_1', 'spfh_2m4_1', 'spfh_2m5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [38]:
# 8
sns.set(), sns.set(font_scale=.75)
columns = ['spfh_2m1_1', 'spfh_2m2_1', 'spfh_2m3_1', 'spfh_2m4_1', 'spfh_2m5_1','ulwrf_s1_1', 'ulwrf_s2_1', 'ulwrf_s3_1', 'ulwrf_s4_1', 'ulwrf_s5_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [39]:
# 9

# sns.set(), sns.set(font_scale=.75)
# columns = ['tmax_2m1_1', 'tmax_2m2_1', 'tmax_2m3_1', 'tmax_2m4_1', 'tmax_2m5_1', 'tmin_2m1_1', 'tmin_2m2_1', 'tmin_2m3_1', 'tmin_2m4_1', 'tmin_2m5_1','tmp_2m_1_1', 'tmp_2m_2_1', 'tmp_2m_3_1', 'tmp_2m_4_1', 'tmp_2m_5_1', 'tmp_sfc1_1', 'tmp_sfc2_1', 'tmp_sfc3_1', 'tmp_sfc4_1', 'tmp_sfc5_1','ulwrf_s1_1', 'ulwrf_s2_1', 'ulwrf_s3_1', 'ulwrf_s4_1', 'ulwrf_s5_1']

# sns.pairplot(train_df[columns], height = 1 ,kind ='scatter',diag_kind='kde')
# plt.show()
In [40]:
# 10

sns.set(), sns.set(font_scale=.75)
columns = ['ulwrf_t1_1', 'ulwrf_t2_1', 'ulwrf_t3_1']

sns.pairplot(train_df[columns], height = 1, kind ='scatter',diag_kind='kde')
plt.show()
In [41]:
# 11

sns.set(), sns.set(font_scale=.75)
columns = ['ulwrf_t4_1', 'ulwrf_t5_1', ]

sns.pairplot(train_df[columns], height = 1 ,kind ='scatter',diag_kind='kde')
plt.show()
In [42]:
# 12

sns.set(), sns.set(font_scale=.75)
columns = ['uswrf_s2_1', 'uswrf_s3_1', 'uswrf_s4_1', 'uswrf_s5_1']

sns.pairplot(train_df[columns], height = 1 ,kind ='scatter',diag_kind='kde')
plt.show()

As we can observe in the graphs above, the most correlated variables present a linear relationship between them. This shows as a diagonal in the graph, since both variables grow at the same time.

4. Train-Test division¶

Since we are working with a time dependent data, we need to avoid mixing it. Also, we are required to add the first 10 years of data to the train set and the last 2 years to the test set. This means we are assigning a 83.333333 of the data to train and a 16.66666666 to test.

Note: This division was already done before the EDA. We overwrite it to start from a clean state.

Note: iloc is useful when we want to split data based on the index or other criteria, while train_test_split is useful when wanting to randomly split data into training and testing subsets.
Therefore, we will use iloc to split the data into train and test sets as we are dealing with time dependent data.

In [43]:
""" Train Test Split (time series) """

# * Make a copy of the dataframe (as Padas dataframe is mutable, therefore uses a reference)
disp_df_copy = disp_df.copy()

# print(disp_df)
# print(disp_df_copy)

# Now we make the train_x, train_y, test_x, test_y splits taking into account the time series
# Note: the time series is ordered by date, therefore we need to split the data in a way that the train data is before the test data
# Note: the 10 first years are used for training and the last two years for testing
# Note: this is done because if not, we will be predicting the past from the future, which leads to errors and overfitting (data leakage) in the model

# * Calculate the number of rows for training and testing
num_rows = disp_df_copy.shape[0]
num_train_rows = int(num_rows * 10/12)  # 10 first years for training, 2 last years for testing

# * Split the data into train and test dataframes (using iloc instead of train_test_split as it picks random rows)
train_df = disp_df_copy.iloc[:num_train_rows, :]  # train contains the first 10 years of rows
test_df = disp_df_copy.iloc[num_train_rows:, :] # test contains the last 2 years of rows

# Print the number of rows for each dataframe
print(f"Number of rows for training: {train_df.shape[0]}")
print(f"Number of rows for testing: {test_df.shape[0]}")

# Print the dataframes
# print(train_df), print(test_df)

# * Separate the input features and target variable for training and testing
X_train = train_df.drop('salida', axis=1)   # By using drop we create a new dataframe without the column 'salida' (train)
y_train = train_df['salida']                # We create a new dataframe with only the column 'salida' (train)
X_test = test_df.drop('salida', axis=1)     # By using drop we create a new dataframe without the column 'salida' (test)
y_test = test_df['salida']                  # We create a new dataframe with only the column 'salida' (test)

# Print the shapes of the dataframes
print(X_train.shape, y_train.shape, X_test.shape, y_test.shape)
Number of rows for training: 3650
Number of rows for testing: 730
(3650, 75) (3650,) (730, 75) (730,)

5. Basic methods:¶

We need to divide the train set using train-test-split in order to simulate the cross validation to get the best hiperparameters. test_size=0.1666666666

Ask if it is needed to scalate the data

In [44]:
from sklearn.preprocessing import StandardScaler 

scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)

5.1. KNN¶

In [45]:
# we create a dictionary to store the results of the models
results = {}
# we create a dictionary to store the times of the models
times = {}

5.1.1. KNN - Predefined parameters¶

The KNN predefinded hyperparameters are the following:

In [46]:
## Evaluation of the model

from sklearn.metrics import mean_squared_error, r2_score
from sklearn.model_selection import TimeSeriesSplit, RandomizedSearchCV, GridSearchCV
from sklearn.neighbors import KNeighborsRegressor
from sklearn.metrics import mean_squared_error, r2_score
import time
In [47]:
param_grid = {'n_neighbors': [5],
              'weights': ['uniform'],
              'metric': ['minkowski']}

## We use TimeSeriesSplit to split the data in folds without losing the temporal order
regr = GridSearchCV(KNeighborsRegressor(), 
                         param_grid,
                         scoring='neg_mean_absolute_error',
                         cv=TimeSeriesSplit(n_splits=5), 
                         n_jobs=1, verbose=1,
                        ## Numero de intentos en cada fold
                        )
start_time = time.time()
regr.fit(X=X_train,y=y_train)
end_time = time.time()
print(regr.best_score_)
results['KNN_pred'] = regr.best_score_

total_time = end_time - start_time
times['KNN_pred'] = total_time
print(f"Execution time: {total_time}s")
Fitting 5 folds for each of 1 candidates, totalling 5 fits
-3152915.546052632
Execution time: 0.1995832920074463s

5.1.2. KNN - Selected parameters¶

In [48]:
import time
budget = 15
param_grid = {'n_neighbors': list(range(1, 50)),
              'weights': ['uniform', 'distance'],
              'metric': ['euclidean', 'manhattan', 'minkowski','chebyshev']}

# ,'mahalanobis'
## We use TimeSeriesSplit to split the data in folds without losing the temporal order
regr = RandomizedSearchCV(KNeighborsRegressor(), 
                         param_grid,
                         scoring='neg_mean_absolute_error', 
                         cv=TimeSeriesSplit(n_splits=5), 
                         n_jobs=1, verbose=1,
                         n_iter=budget
                        ## Numero de intentos en cada fold
                        )
start_time = time.time()
regr.fit(X=X_train,y=y_train)
end_time = time.time()
print(regr.best_score_)
results['KNN_select'] = regr.best_score_

total_time = end_time - start_time
times['KNN_select'] = total_time
print(f"Execution time: {total_time}s")
Fitting 5 folds for each of 15 candidates, totalling 75 fits
-2943689.2433133833
Execution time: 1.952528715133667s

5.2 Regression Trees¶

5.2.1. Regression Trees - Predefined parameters¶

In [49]:
from sklearn.tree import DecisionTreeRegressor
import time

param_grid = {'criterion' : ["squared_error"],
              'splitter' : ["best"],              
              'min_samples_split' : [2]}

## We use TimeSeriesSplit to split the data in folds without losing the temporal order
regr = GridSearchCV(DecisionTreeRegressor(), 
                         param_grid,
                         scoring='neg_mean_absolute_error',
                         cv=TimeSeriesSplit(n_splits=5), 
                         n_jobs=1, verbose=1,
                        ## Numero de intentos en cada fold
                        )
start_time = time.time()
regr.fit(X=X_train,y=y_train)
end_time = time.time()
print(regr.best_score_)
results['RegTrees_pred'] = regr.best_score_

total_time = end_time - start_time
times['RegTrees_pred'] = total_time
print(f"Execution time: {total_time}s")
Fitting 5 folds for each of 1 candidates, totalling 5 fits
-3404937.335526316
Execution time: 0.7049572467803955s

5.2.2. Regression Trees - Selected parameters¶

In [59]:
from sklearn.tree import DecisionTreeRegressor
import time
budget = 15

param_grid = {'criterion' : ["absolute_error", "squared_error"],
              'splitter' : ["best", "random"],
              'max_depth' : list(range(1, 40)),
              'min_samples_split' : list(range(5, 200)),
              'max_features' : ["sqrt", "log2", None]}

# We use TimeSeriesSplit to split the data in folds without losing the temporal order
regr = RandomizedSearchCV(DecisionTreeRegressor(), 
                         param_grid,
                         scoring='neg_mean_absolute_error',
                         cv=TimeSeriesSplit(n_splits=5),
                         n_jobs=1, verbose=1,
                         n_iter=budget
)

start_time = time.time()                      
regr.fit(X=X_train,y=y_train)
end_time = time.time()

# We print all the scores
print(regr.best_params_)
print(regr.best_score_) 
results['RegTrees_select'] = regr.best_score_

total_time = end_time - start_time
times['RegTrees_select'] = total_time
print(f"Execution time: {total_time}s")
Fitting 5 folds for each of 15 candidates, totalling 75 fits
{'splitter': 'random', 'min_samples_split': 123, 'max_features': None, 'max_depth': 24, 'criterion': 'absolute_error'}
-2784490.509868421
Execution time: 15.269333362579346s

5.3 Linnear regression¶

5.3.1. Linear regression - Predefined parameters¶

In [51]:
from sklearn.linear_model import LinearRegression
import time

param_grid = {'fit_intercept': [True]}


regr = GridSearchCV(LinearRegression(),
                    param_grid,
                    scoring='neg_mean_absolute_error',
                    cv=TimeSeriesSplit(n_splits=5),
                    n_jobs=1, verbose=1,
                    )
start_time = time.time()
regr.fit(X=X_train, y=y_train)
end_time = time.time()
print(regr.best_score_)

results['LinearReg_pred'] = regr.best_score_

total_time = end_time - start_time
times['LinearReg_pred'] = total_time
print(f"Execution time: {total_time}s")
Fitting 5 folds for each of 1 candidates, totalling 5 fits
-2437056.0592060336
Execution time: 0.32973408699035645s

5.3.2. Linear regression - Selected parameters¶

In [52]:
from sklearn.linear_model import LinearRegression, Lasso, Ridge, ElasticNet
import time
import random

all_scores = []

param_lasso= {'alpha': [0.0001, 0.0005, 0.0003, 0.001, 0.0015, 0.002, 0.005, 0.01, 0.1, 1]}
param_ridge= {'alpha': [0.0001, 0.0005, 0.0003, 0.001, 0.0015, 0.002, 0.005, 0.01, 0.1, 1]}
param_elastic= {'alpha': [0.0001, 0.0005, 0.0003, 0.001, 0.0015, 0.002, 0.005, 0.01, 0.1, 1],
                'l1_ratio': [0.0001, 0.0005, 0.0003, 0.001, 0.0015, 0.002, 0.005, 0.01, 0.1, 0.5, 0.9, 0.99]}
budget = 10
n_splits = 5

regr_lasso = RandomizedSearchCV(Lasso(fit_intercept=True, tol=0.1),
                                param_lasso,
                                scoring='neg_mean_absolute_error',
                                cv=TimeSeriesSplit(),
                                n_jobs=1, verbose=1,
                                n_iter=budget,
                                )

regr_ridge = RandomizedSearchCV(Ridge(fit_intercept=True),
                                param_ridge,
                                scoring='neg_mean_absolute_error',
                                cv=TimeSeriesSplit(),
                                n_jobs=1, verbose=1,
                                n_iter=budget,
                                )

regr_elastic = RandomizedSearchCV(ElasticNet(fit_intercept=True, tol=0.1),
                                  param_elastic,
                                  scoring='neg_mean_absolute_error',
                                  cv=TimeSeriesSplit(),
                                  n_jobs=1, verbose=1,
                                  n_iter=budget,
                                  )

# ! If we want to use random values for the parameters -> unconsistency in the results
# regr_lasso = RandomizedSearchCV(Lasso(fit_intercept=True, tol=0.1),
#                                 {'alpha': [random.uniform(0.0001, 0.1) for i in range(50)]},
#                                 scoring='neg_mean_absolute_error',
#                                 cv=TimeSeriesSplit(),
#                                 n_jobs=1, verbose=1,
#                                 n_iter=budget,
#                                 )

# regr_ridge = RandomizedSearchCV(Ridge(fit_intercept=True),
#                                 {'alpha': [random.uniform(0.0001, 0.1) for i in range(50)]},
#                                 scoring='neg_mean_absolute_error',
#                                 cv=TimeSeriesSplit(),
#                                 n_jobs=1, verbose=1,
#                                 n_iter=budget,
#                                 )

# regr_elastic = RandomizedSearchCV(ElasticNet(fit_intercept=True, tol=0.1),
#                                   {'alpha': [random.uniform(0.0001, 0.1) for i in range(50)],
#                                   'l1_ratio': [random.uniform(0.001, 1) for i in range(50)]},
#                                   scoring='neg_mean_absolute_error',
#                                   cv=TimeSeriesSplit(),
#                                   n_jobs=1, verbose=1,
#                                   n_iter=budget,
#                                   )

regr = [regr_lasso, regr_ridge, regr_elastic]

start_time = time.time()
for i in regr:
    i.fit(X=X_train,y=y_train)
    all_scores.append(i.best_score_)
end_time = time.time()

max_score = max(all_scores)
best_regr = regr[all_scores.index(max_score)]
total_time = end_time - start_time
results['LinearReg_select'] = max_score
times['LinearReg_select'] = total_time

print(all_scores)
print(best_regr.best_estimator_)
print(best_regr.best_params_)
print(max_score)
print(f"Execution time: {total_time}s")
Fitting 5 folds for each of 10 candidates, totalling 50 fits
Fitting 5 folds for each of 10 candidates, totalling 50 fits
Fitting 5 folds for each of 10 candidates, totalling 50 fits
[-2608743.50698319, -2435388.9447004595, -2559008.5143872397]
Ridge(alpha=0.001)
{'alpha': 0.001}
-2435388.9447004595
Execution time: 1.1082279682159424s

5.4. Results¶

In [53]:
# ! Obtain best, worst, fastest and slowest model
max_score = max(results.values())
min_score = min(results.values())
max_time = max(times.values())
min_time = min(times.values())

best_model = list(results.keys())[list(results.values()).index(max_score)]
worst_model = list(results.keys())[list(results.values()).index(min_score)]
fastest_model = list(times.keys())[list(times.values()).index(min_time)]
slowest_model = list(times.keys())[list(times.values()).index(max_time)]

print(f"Best model: {best_model} with score {abs(max_score)} and time {list(times.values())[list(results.values()).index(max_score)]} s")
print(f"Worst model: {worst_model} with score {abs(min_score)} and time {list(times.values())[list(results.values()).index(min_score)]} s")
print(f"Fastest model: {fastest_model} with score {abs(list(results.values())[list(times.values()).index(min_time)])} and time {min_time} s")
print(f"Slowest model: {slowest_model} with score {abs(list(results.values())[list(times.values()).index(max_time)])} and time {max_time} s")

# ! Average score of the models
avg_score = 0
avg_time = 0

for key, value in results.items():
    avg_score += value
    avg_time += times[key]

print(f"\nAverage score: {abs(avg_score/len(results))}")
print(f"Average time: {avg_time/len(times)}\n")


# ! Differences
print("The score difference between the best and worst model is: ", abs(max_score - min_score))
print("The score difference between the best and fastest model is: ", abs(max_score - list(results.values())[list(times.values()).index(min_time)]))
print("The time difference between the best and fastest model model is: ", abs(list(times.values())[list(results.values()).index(max_score)] - min_time))
print("The time difference between the fastest and slowest model is: ", abs(max_time - min_time))
Best model: LinearReg_select with score 2435388.9447004595 and time 1.1082279682159424 s
Worst model: RegTrees_pred with score 3404937.335526316 and time 0.7049572467803955 s
Fastest model: KNN_pred with score 3152915.546052632 and time 0.1995832920074463 s
Slowest model: RegTrees_select with score 2833502.0454524304 and time 10.439216375350952 s

Average score: 2867914.862375209
Average time: 2.4557079474131265

The score difference between the best and worst model is:  969548.3908258565
The score difference between the best and fastest model is:  717526.6013521724
The time difference between the best and fastest model model is:  0.9086446762084961
The time difference between the fastest and slowest model is:  10.239633083343506

5.5. Conclusions:¶

After computig the models we can see that the best model in terms of MAe is the LinearReg_selected, but the best timing model is LinearReg_pred.

*Obtener algunas conclusiones, tales como: ¿cuál es el mejor método? ¿Cuál de los métodos básicos de aprendizaje automático es más rápido? ¿Los resultados son mejores que los regresores triviales/naive/baseline? ¿El ajuste de hiperparámetros mejora con respecto a los valores por omisión? ¿Hay algún equilibrio entre tiempo de ejecución y mejora de resultados? Etc*

X. Output the Jupyter Notebook as an HTML file¶

In [54]:
import os

# Export the notebook to HTML
os.system('jupyter nbconvert --to html model.ipynb --output ../data/html/model.html')
print("Notebook exported to HTML")
[NbConvertApp] Converting notebook model.ipynb to html
Notebook exported to HTML
[NbConvertApp] Writing 5935001 bytes to ../data/html/model.html